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<h1 class="epydoc">Source Code for <a href="peach.optm.linear-module.html">Module peach.optm.linear</a></h1>
<pre class="py-src">
<a name="L1"></a><tt class="py-lineno">  1</tt>  <tt class="py-line"><tt class="py-comment">################################################################################</tt> </tt>
<a name="L2"></a><tt class="py-lineno">  2</tt>  <tt class="py-line"><tt class="py-comment"># Peach - Computational Intelligence for Python</tt> </tt>
<a name="L3"></a><tt class="py-lineno">  3</tt>  <tt class="py-line"><tt class="py-comment"># Jose Alexandre Nalon</tt> </tt>
<a name="L4"></a><tt class="py-lineno">  4</tt>  <tt class="py-line"><tt class="py-comment">#</tt> </tt>
<a name="L5"></a><tt class="py-lineno">  5</tt>  <tt class="py-line"><tt class="py-comment"># This file: optm/linear.py</tt> </tt>
<a name="L6"></a><tt class="py-lineno">  6</tt>  <tt class="py-line"><tt class="py-comment"># 1D search methods</tt> </tt>
<a name="L7"></a><tt class="py-lineno">  7</tt>  <tt class="py-line"><tt class="py-comment">################################################################################</tt> </tt>
<a name="L8"></a><tt class="py-lineno">  8</tt>  <tt class="py-line"> </tt>
<a name="L9"></a><tt class="py-lineno">  9</tt>  <tt class="py-line"><tt class="py-comment"># Doc string, reStructuredText formatted:</tt> </tt>
<a name="L10"></a><tt class="py-lineno"> 10</tt>  <tt class="py-line"><tt id="link-0" class="py-name" targets="Variable peach.__doc__=peach-module.html#__doc__,Variable peach.fuzzy.__doc__=peach.fuzzy-module.html#__doc__,Variable peach.fuzzy.base.__doc__=peach.fuzzy.base-module.html#__doc__,Variable peach.fuzzy.cmeans.__doc__=peach.fuzzy.cmeans-module.html#__doc__,Variable peach.fuzzy.control.__doc__=peach.fuzzy.control-module.html#__doc__,Variable peach.fuzzy.defuzzy.__doc__=peach.fuzzy.defuzzy-module.html#__doc__,Variable peach.fuzzy.mf.__doc__=peach.fuzzy.mf-module.html#__doc__,Variable peach.fuzzy.norms.__doc__=peach.fuzzy.norms-module.html#__doc__,Variable peach.ga.__doc__=peach.ga-module.html#__doc__,Variable peach.ga.base.__doc__=peach.ga.base-module.html#__doc__,Variable peach.ga.chromosome.__doc__=peach.ga.chromosome-module.html#__doc__,Variable peach.ga.crossover.__doc__=peach.ga.crossover-module.html#__doc__,Variable peach.ga.fitness.__doc__=peach.ga.fitness-module.html#__doc__,Variable peach.ga.mutation.__doc__=peach.ga.mutation-module.html#__doc__,Variable peach.ga.selection.__doc__=peach.ga.selection-module.html#__doc__,Variable peach.nn.__doc__=peach.nn-module.html#__doc__,Variable peach.nn.af.__doc__=peach.nn.af-module.html#__doc__,Variable peach.nn.base.__doc__=peach.nn.base-module.html#__doc__,Variable peach.nn.kmeans.__doc__=peach.nn.kmeans-module.html#__doc__,Variable peach.nn.lrules.__doc__=peach.nn.lrules-module.html#__doc__,Variable peach.nn.mem.__doc__=peach.nn.mem-module.html#__doc__,Variable peach.nn.nnet.__doc__=peach.nn.nnet-module.html#__doc__,Variable peach.nn.rbfn.__doc__=peach.nn.rbfn-module.html#__doc__,Variable peach.optm.__doc__=peach.optm-module.html#__doc__,Variable peach.optm.base.__doc__=peach.optm.base-module.html#__doc__,Variable peach.optm.linear.__doc__=peach.optm.linear-module.html#__doc__,Variable peach.optm.multivar.__doc__=peach.optm.multivar-module.html#__doc__,Variable peach.optm.quasinewton.__doc__=peach.optm.quasinewton-module.html#__doc__,Variable peach.optm.stochastic.__doc__=peach.optm.stochastic-module.html#__doc__,Variable peach.pso.__doc__=peach.pso-module.html#__doc__,Variable peach.pso.acc.__doc__=peach.pso.acc-module.html#__doc__,Variable peach.pso.base.__doc__=peach.pso.base-module.html#__doc__,Variable peach.sa.__doc__=peach.sa-module.html#__doc__,Variable peach.sa.base.__doc__=peach.sa.base-module.html#__doc__,Variable peach.sa.neighbor.__doc__=peach.sa.neighbor-module.html#__doc__"><a title="peach.__doc__
peach.fuzzy.__doc__
peach.fuzzy.base.__doc__
peach.fuzzy.cmeans.__doc__
peach.fuzzy.control.__doc__
peach.fuzzy.defuzzy.__doc__
peach.fuzzy.mf.__doc__
peach.fuzzy.norms.__doc__
peach.ga.__doc__
peach.ga.base.__doc__
peach.ga.chromosome.__doc__
peach.ga.crossover.__doc__
peach.ga.fitness.__doc__
peach.ga.mutation.__doc__
peach.ga.selection.__doc__
peach.nn.__doc__
peach.nn.af.__doc__
peach.nn.base.__doc__
peach.nn.kmeans.__doc__
peach.nn.lrules.__doc__
peach.nn.mem.__doc__
peach.nn.nnet.__doc__
peach.nn.rbfn.__doc__
peach.optm.__doc__
peach.optm.base.__doc__
peach.optm.linear.__doc__
peach.optm.multivar.__doc__
peach.optm.quasinewton.__doc__
peach.optm.stochastic.__doc__
peach.pso.__doc__
peach.pso.acc.__doc__
peach.pso.base.__doc__
peach.sa.__doc__
peach.sa.base.__doc__
peach.sa.neighbor.__doc__" class="py-name" href="#" onclick="return doclink('link-0', '__doc__', 'link-0');">__doc__</a></tt> <tt class="py-op">=</tt> <tt class="py-docstring">"""</tt> </tt>
<a name="L11"></a><tt class="py-lineno"> 11</tt>  <tt class="py-line"><tt class="py-docstring">This package implements basic one variable only optimizers.</tt> </tt>
<a name="L12"></a><tt class="py-lineno"> 12</tt>  <tt class="py-line"><tt class="py-docstring">"""</tt> </tt>
<a name="L13"></a><tt class="py-lineno"> 13</tt>  <tt class="py-line"> </tt>
<a name="L14"></a><tt class="py-lineno"> 14</tt>  <tt class="py-line"> </tt>
<a name="L15"></a><tt class="py-lineno"> 15</tt>  <tt class="py-line"><tt class="py-comment">################################################################################</tt> </tt>
<a name="L16"></a><tt class="py-lineno"> 16</tt>  <tt class="py-line"><tt class="py-keyword">from</tt> <tt class="py-name">numpy</tt> <tt class="py-keyword">import</tt> <tt id="link-1" class="py-name" targets="Variable peach.nn.rbfn.abs=peach.nn.rbfn-module.html#abs,Variable peach.pso.base.abs=peach.pso.base-module.html#abs"><a title="peach.nn.rbfn.abs
peach.pso.base.abs" class="py-name" href="#" onclick="return doclink('link-1', 'abs', 'link-1');">abs</a></tt><tt class="py-op">,</tt> <tt class="py-name">max</tt> </tt>
<a name="L17"></a><tt class="py-lineno"> 17</tt>  <tt class="py-line"><tt class="py-keyword">from</tt> <tt id="link-2" class="py-name" targets="Module peach.fuzzy.base=peach.fuzzy.base-module.html,Module peach.ga.base=peach.ga.base-module.html,Module peach.nn.base=peach.nn.base-module.html,Module peach.optm.base=peach.optm.base-module.html,Module peach.pso.base=peach.pso.base-module.html,Module peach.sa.base=peach.sa.base-module.html"><a title="peach.fuzzy.base
peach.ga.base
peach.nn.base
peach.optm.base
peach.pso.base
peach.sa.base" class="py-name" href="#" onclick="return doclink('link-2', 'base', 'link-2');">base</a></tt> <tt class="py-keyword">import</tt> <tt id="link-3" class="py-name" targets="Class peach.optm.base.Optimizer=peach.optm.base.Optimizer-class.html"><a title="peach.optm.base.Optimizer" class="py-name" href="#" onclick="return doclink('link-3', 'Optimizer', 'link-3');">Optimizer</a></tt> </tt>
<a name="L18"></a><tt class="py-lineno"> 18</tt>  <tt class="py-line"> </tt>
<a name="L19"></a><tt class="py-lineno"> 19</tt>  <tt class="py-line"> </tt>
<a name="L20"></a><tt class="py-lineno"> 20</tt>  <tt class="py-line"><tt class="py-comment">################################################################################</tt> </tt>
<a name="L21"></a><tt class="py-lineno"> 21</tt>  <tt class="py-line"><tt class="py-comment"># Classes</tt> </tt>
<a name="L22"></a><tt class="py-lineno"> 22</tt>  <tt class="py-line"><tt class="py-comment">################################################################################</tt> </tt>
<a name="Direct1D"></a><div id="Direct1D-def"><a name="L23"></a><tt class="py-lineno"> 23</tt> <a class="py-toggle" href="#" id="Direct1D-toggle" onclick="return toggle('Direct1D');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="peach.optm.linear.Direct1D-class.html">Direct1D</a><tt class="py-op">(</tt><tt class="py-base-class">Optimizer</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Direct1D-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="Direct1D-expanded"><a name="L24"></a><tt class="py-lineno"> 24</tt>  <tt class="py-line">    <tt class="py-docstring">'''</tt> </tt>
<a name="L25"></a><tt class="py-lineno"> 25</tt>  <tt class="py-line"><tt class="py-docstring">    1-D direct search.</tt> </tt>
<a name="L26"></a><tt class="py-lineno"> 26</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L27"></a><tt class="py-lineno"> 27</tt>  <tt class="py-line"><tt class="py-docstring">    This methods 'oscilates' around the function minimum, reducing the updating</tt> </tt>
<a name="L28"></a><tt class="py-lineno"> 28</tt>  <tt class="py-line"><tt class="py-docstring">    step until it achieves the maximum error or the maximum number of steps.</tt> </tt>
<a name="L29"></a><tt class="py-lineno"> 29</tt>  <tt class="py-line"><tt class="py-docstring">    This is a very inefficient method, and should be used only at times where no</tt> </tt>
<a name="L30"></a><tt class="py-lineno"> 30</tt>  <tt class="py-line"><tt class="py-docstring">    other methods are able to converge (eg., if a function has a lot of</tt> </tt>
<a name="L31"></a><tt class="py-lineno"> 31</tt>  <tt class="py-line"><tt class="py-docstring">    discontinuities, or similar conditions).</tt> </tt>
<a name="L32"></a><tt class="py-lineno"> 32</tt>  <tt class="py-line"><tt class="py-docstring">    '''</tt> </tt>
<a name="Direct1D.__init__"></a><div id="Direct1D.__init__-def"><a name="L33"></a><tt class="py-lineno"> 33</tt> <a class="py-toggle" href="#" id="Direct1D.__init__-toggle" onclick="return toggle('Direct1D.__init__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="peach.optm.linear.Direct1D-class.html#__init__">__init__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">f</tt><tt class="py-op">,</tt> <tt class="py-param">x0</tt><tt class="py-op">,</tt> <tt class="py-param">range</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt> <tt class="py-param">h</tt><tt class="py-op">=</tt><tt class="py-number">0.5</tt><tt class="py-op">,</tt> <tt class="py-param">emax</tt><tt class="py-op">=</tt><tt class="py-number">1e-8</tt><tt class="py-op">,</tt> <tt class="py-param">imax</tt><tt class="py-op">=</tt><tt class="py-number">1000</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Direct1D.__init__-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Direct1D.__init__-expanded"><a name="L34"></a><tt class="py-lineno"> 34</tt>  <tt class="py-line">        <tt class="py-docstring">'''</tt> </tt>
<a name="L35"></a><tt class="py-lineno"> 35</tt>  <tt class="py-line"><tt class="py-docstring">        Initializes the optimizer.</tt> </tt>
<a name="L36"></a><tt class="py-lineno"> 36</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L37"></a><tt class="py-lineno"> 37</tt>  <tt class="py-line"><tt class="py-docstring">        To create an optimizer of this type, instantiate the class with the</tt> </tt>
<a name="L38"></a><tt class="py-lineno"> 38</tt>  <tt class="py-line"><tt class="py-docstring">        parameters given below:</tt> </tt>
<a name="L39"></a><tt class="py-lineno"> 39</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L40"></a><tt class="py-lineno"> 40</tt>  <tt class="py-line"><tt class="py-docstring">        :Parameters:</tt> </tt>
<a name="L41"></a><tt class="py-lineno"> 41</tt>  <tt class="py-line"><tt class="py-docstring">          f</tt> </tt>
<a name="L42"></a><tt class="py-lineno"> 42</tt>  <tt class="py-line"><tt class="py-docstring">            A one variable only function to be optimized. The function should</tt> </tt>
<a name="L43"></a><tt class="py-lineno"> 43</tt>  <tt class="py-line"><tt class="py-docstring">            have only one parameter and return the function value.</tt> </tt>
<a name="L44"></a><tt class="py-lineno"> 44</tt>  <tt class="py-line"><tt class="py-docstring">          x0</tt> </tt>
<a name="L45"></a><tt class="py-lineno"> 45</tt>  <tt class="py-line"><tt class="py-docstring">            First estimate of the minimum. Since this is a linear method, this</tt> </tt>
<a name="L46"></a><tt class="py-lineno"> 46</tt>  <tt class="py-line"><tt class="py-docstring">            should be a ``float`` or ``int``.</tt> </tt>
<a name="L47"></a><tt class="py-lineno"> 47</tt>  <tt class="py-line"><tt class="py-docstring">          range</tt> </tt>
<a name="L48"></a><tt class="py-lineno"> 48</tt>  <tt class="py-line"><tt class="py-docstring">            A range of values might be passed to the algorithm, but it is not</tt> </tt>
<a name="L49"></a><tt class="py-lineno"> 49</tt>  <tt class="py-line"><tt class="py-docstring">            necessary. If supplied, this parameter should be a tuples of two</tt> </tt>
<a name="L50"></a><tt class="py-lineno"> 50</tt>  <tt class="py-line"><tt class="py-docstring">            values, ``(x0, x1)``, where ``x0`` is the start of the interval, and</tt> </tt>
<a name="L51"></a><tt class="py-lineno"> 51</tt>  <tt class="py-line"><tt class="py-docstring">            ``x1`` its end. Obviously, ``x0`` should be smaller than ``x1``.</tt> </tt>
<a name="L52"></a><tt class="py-lineno"> 52</tt>  <tt class="py-line"><tt class="py-docstring">            When this parameter is present, the algorithm will not let the</tt> </tt>
<a name="L53"></a><tt class="py-lineno"> 53</tt>  <tt class="py-line"><tt class="py-docstring">            estimates fall outside the given interval.</tt> </tt>
<a name="L54"></a><tt class="py-lineno"> 54</tt>  <tt class="py-line"><tt class="py-docstring">          h</tt> </tt>
<a name="L55"></a><tt class="py-lineno"> 55</tt>  <tt class="py-line"><tt class="py-docstring">            The initial step of the search. Defaults to 0.5</tt> </tt>
<a name="L56"></a><tt class="py-lineno"> 56</tt>  <tt class="py-line"><tt class="py-docstring">          emax</tt> </tt>
<a name="L57"></a><tt class="py-lineno"> 57</tt>  <tt class="py-line"><tt class="py-docstring">            Maximum allowed error. The algorithm stops as soon as the error is</tt> </tt>
<a name="L58"></a><tt class="py-lineno"> 58</tt>  <tt class="py-line"><tt class="py-docstring">            below this level. The error is absolute.</tt> </tt>
<a name="L59"></a><tt class="py-lineno"> 59</tt>  <tt class="py-line"><tt class="py-docstring">          imax</tt> </tt>
<a name="L60"></a><tt class="py-lineno"> 60</tt>  <tt class="py-line"><tt class="py-docstring">            Maximum number of iterations, the algorithm stops as soon this</tt> </tt>
<a name="L61"></a><tt class="py-lineno"> 61</tt>  <tt class="py-line"><tt class="py-docstring">            number of iterations are executed, no matter what the error is at</tt> </tt>
<a name="L62"></a><tt class="py-lineno"> 62</tt>  <tt class="py-line"><tt class="py-docstring">            the moment.</tt> </tt>
<a name="L63"></a><tt class="py-lineno"> 63</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L64"></a><tt class="py-lineno"> 64</tt>  <tt class="py-line">        <tt id="link-4" class="py-name"><a title="peach.optm.base.Optimizer" class="py-name" href="#" onclick="return doclink('link-4', 'Optimizer', 'link-3');">Optimizer</a></tt><tt class="py-op">.</tt><tt id="link-5" class="py-name" targets="Method peach.fuzzy.base.FuzzySet.__init__()=peach.fuzzy.base.FuzzySet-class.html#__init__,Method peach.fuzzy.cmeans.FuzzyCMeans.__init__()=peach.fuzzy.cmeans.FuzzyCMeans-class.html#__init__,Method peach.fuzzy.control.Controller.__init__()=peach.fuzzy.control.Controller-class.html#__init__,Method peach.fuzzy.control.Parametric.__init__()=peach.fuzzy.control.Parametric-class.html#__init__,Method peach.fuzzy.mf.Bell.__init__()=peach.fuzzy.mf.Bell-class.html#__init__,Method peach.fuzzy.mf.DecreasingRamp.__init__()=peach.fuzzy.mf.DecreasingRamp-class.html#__init__,Method peach.fuzzy.mf.DecreasingSigmoid.__init__()=peach.fuzzy.mf.DecreasingSigmoid-class.html#__init__,Method peach.fuzzy.mf.Gaussian.__init__()=peach.fuzzy.mf.Gaussian-class.html#__init__,Method peach.fuzzy.mf.IncreasingRamp.__init__()=peach.fuzzy.mf.IncreasingRamp-class.html#__init__,Method peach.fuzzy.mf.IncreasingSigmoid.__init__()=peach.fuzzy.mf.IncreasingSigmoid-class.html#__init__,Method peach.fuzzy.mf.Membership.__init__()=peach.fuzzy.mf.Membership-class.html#__init__,Method peach.fuzzy.mf.RaisedCosine.__init__()=peach.fuzzy.mf.RaisedCosine-class.html#__init__,Method peach.fuzzy.mf.Smf.__init__()=peach.fuzzy.mf.Smf-class.html#__init__,Method peach.fuzzy.mf.Trapezoid.__init__()=peach.fuzzy.mf.Trapezoid-class.html#__init__,Method peach.fuzzy.mf.Triangle.__init__()=peach.fuzzy.mf.Triangle-class.html#__init__,Method peach.fuzzy.mf.Zmf.__init__()=peach.fuzzy.mf.Zmf-class.html#__init__,Method peach.ga.base.GeneticAlgorithm.__init__()=peach.ga.base.GeneticAlgorithm-class.html#__init__,Method peach.ga.chromosome.Chromosome.__init__()=peach.ga.chromosome.Chromosome-class.html#__init__,Method peach.ga.crossover.OnePoint.__init__()=peach.ga.crossover.OnePoint-class.html#__init__,Method peach.ga.crossover.TwoPoint.__init__()=peach.ga.crossover.TwoPoint-class.html#__init__,Method peach.ga.crossover.Uniform.__init__()=peach.ga.crossover.Uniform-class.html#__init__,Method peach.ga.fitness.Fitness.__init__()=peach.ga.fitness.Fitness-class.html#__init__,Method peach.ga.fitness.Ranking.__init__()=peach.ga.fitness.Ranking-class.html#__init__,Method peach.ga.mutation.BitToBit.__init__()=peach.ga.mutation.BitToBit-class.html#__init__,Method peach.nn.af.Activation.__init__()=peach.nn.af.Activation-class.html#__init__,Method peach.nn.af.ArcTan.__init__()=peach.nn.af.ArcTan-class.html#__init__,Method peach.nn.af.Gaussian.__init__()=peach.nn.af.Gaussian-class.html#__init__,Method peach.nn.af.Linear.__init__()=peach.nn.af.Linear-class.html#__init__,Method peach.nn.af.Ramp.__init__()=peach.nn.af.Ramp-class.html#__init__,Method 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peach.sa.neighbor.UniformNeighbor.__init__" class="py-name" href="#" onclick="return doclink('link-5', '__init__', 'link-5');">__init__</a></tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">)</tt> </tt>
<a name="L65"></a><tt class="py-lineno"> 65</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__f</tt> <tt class="py-op">=</tt> <tt class="py-name">f</tt> </tt>
<a name="L66"></a><tt class="py-lineno"> 66</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt> <tt class="py-op">=</tt> <tt class="py-name">x0</tt> </tt>
<a name="L67"></a><tt class="py-lineno"> 67</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">range</tt> <tt class="py-op">=</tt> <tt class="py-name">range</tt> </tt>
<a name="L68"></a><tt class="py-lineno"> 68</tt>  <tt class="py-line">        <tt class="py-string">'''Holds the range for the estimates. If this attribute is set, the</tt> </tt>
<a name="L69"></a><tt class="py-lineno"> 69</tt>  <tt class="py-line"><tt class="py-string">        algorithm will never let the estimates fall outside the given</tt> </tt>
<a name="L70"></a><tt class="py-lineno"> 70</tt>  <tt class="py-line"><tt class="py-string">        interval.'''</tt> </tt>
<a name="L71"></a><tt class="py-lineno"> 71</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__h</tt> <tt class="py-op">=</tt> <tt class="py-name">h</tt> </tt>
<a name="L72"></a><tt class="py-lineno"> 72</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__emax</tt> <tt class="py-op">=</tt> <tt class="py-name">float</tt><tt class="py-op">(</tt><tt class="py-name">emax</tt><tt class="py-op">)</tt> </tt>
<a name="L73"></a><tt class="py-lineno"> 73</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__imax</tt> <tt class="py-op">=</tt> <tt class="py-name">int</tt><tt class="py-op">(</tt><tt class="py-name">imax</tt><tt class="py-op">)</tt> </tt>
</div><a name="L74"></a><tt class="py-lineno"> 74</tt>  <tt class="py-line"> </tt>
<a name="L75"></a><tt class="py-lineno"> 75</tt>  <tt class="py-line"> </tt>
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</div><div id="Direct1D.__get_x-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Direct1D.__get_x-expanded"><a name="L77"></a><tt class="py-lineno"> 77</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt> </tt>
</div><a name="L78"></a><tt class="py-lineno"> 78</tt>  <tt class="py-line"> </tt>
<a name="Direct1D.__set_x"></a><div id="Direct1D.__set_x-def"><a name="L79"></a><tt class="py-lineno"> 79</tt> <a class="py-toggle" href="#" id="Direct1D.__set_x-toggle" onclick="return toggle('Direct1D.__set_x');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="peach.optm.linear.Direct1D-class.html#__set_x">__set_x</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x0</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
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<a name="L83"></a><tt class="py-lineno"> 83</tt>  <tt class="py-line">    <tt class="py-string">'''The estimate of the position of the minimum.'''</tt> </tt>
<a name="L84"></a><tt class="py-lineno"> 84</tt>  <tt class="py-line"> </tt>
<a name="L85"></a><tt class="py-lineno"> 85</tt>  <tt class="py-line"> </tt>
<a name="Direct1D.restart"></a><div id="Direct1D.restart-def"><a name="L86"></a><tt class="py-lineno"> 86</tt> <a class="py-toggle" href="#" id="Direct1D.restart-toggle" onclick="return toggle('Direct1D.restart');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="peach.optm.linear.Direct1D-class.html#restart">restart</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x0</tt><tt class="py-op">,</tt> <tt class="py-param">h</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Direct1D.restart-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Direct1D.restart-expanded"><a name="L87"></a><tt class="py-lineno"> 87</tt>  <tt class="py-line">        <tt class="py-docstring">'''</tt> </tt>
<a name="L88"></a><tt class="py-lineno"> 88</tt>  <tt class="py-line"><tt class="py-docstring">        Resets the optimizer, returning to its original state, and allowing to</tt> </tt>
<a name="L89"></a><tt class="py-lineno"> 89</tt>  <tt class="py-line"><tt class="py-docstring">        use a new first estimate.</tt> </tt>
<a name="L90"></a><tt class="py-lineno"> 90</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L91"></a><tt class="py-lineno"> 91</tt>  <tt class="py-line"><tt class="py-docstring">        :Parameters:</tt> </tt>
<a name="L92"></a><tt class="py-lineno"> 92</tt>  <tt class="py-line"><tt class="py-docstring">          x0</tt> </tt>
<a name="L93"></a><tt class="py-lineno"> 93</tt>  <tt class="py-line"><tt class="py-docstring">            The new initial value of the estimate of the minimum. Since this is</tt> </tt>
<a name="L94"></a><tt class="py-lineno"> 94</tt>  <tt class="py-line"><tt class="py-docstring">            a linear method, this should be a ``float`` or ``int``.</tt> </tt>
<a name="L95"></a><tt class="py-lineno"> 95</tt>  <tt class="py-line"><tt class="py-docstring">          h</tt> </tt>
<a name="L96"></a><tt class="py-lineno"> 96</tt>  <tt class="py-line"><tt class="py-docstring">            The initial step of the search. Defaults to 0.5</tt> </tt>
<a name="L97"></a><tt class="py-lineno"> 97</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L98"></a><tt class="py-lineno"> 98</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt> <tt class="py-op">=</tt> <tt class="py-name">x0</tt> </tt>
<a name="L99"></a><tt class="py-lineno"> 99</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">h</tt> <tt class="py-keyword">is</tt> <tt class="py-keyword">not</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> </tt>
<a name="L100"></a><tt class="py-lineno">100</tt>  <tt class="py-line">            <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__h</tt> <tt class="py-op">=</tt> <tt class="py-name">h</tt> </tt>
</div><a name="L101"></a><tt class="py-lineno">101</tt>  <tt class="py-line"> </tt>
<a name="L102"></a><tt class="py-lineno">102</tt>  <tt class="py-line"> </tt>
<a name="Direct1D.step"></a><div id="Direct1D.step-def"><a name="L103"></a><tt class="py-lineno">103</tt> <a class="py-toggle" href="#" id="Direct1D.step-toggle" onclick="return toggle('Direct1D.step');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="peach.optm.linear.Direct1D-class.html#step">step</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Direct1D.step-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Direct1D.step-expanded"><a name="L104"></a><tt class="py-lineno">104</tt>  <tt class="py-line">        <tt class="py-docstring">'''</tt> </tt>
<a name="L105"></a><tt class="py-lineno">105</tt>  <tt class="py-line"><tt class="py-docstring">        One step of the search.</tt> </tt>
<a name="L106"></a><tt class="py-lineno">106</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L107"></a><tt class="py-lineno">107</tt>  <tt class="py-line"><tt class="py-docstring">        In this method, the result of the step is highly dependent of the steps</tt> </tt>
<a name="L108"></a><tt class="py-lineno">108</tt>  <tt class="py-line"><tt class="py-docstring">        executed before, as the search step is updated at each call to this</tt> </tt>
<a name="L109"></a><tt class="py-lineno">109</tt>  <tt class="py-line"><tt class="py-docstring">        method.</tt> </tt>
<a name="L110"></a><tt class="py-lineno">110</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L111"></a><tt class="py-lineno">111</tt>  <tt class="py-line"><tt class="py-docstring">        :Returns:</tt> </tt>
<a name="L112"></a><tt class="py-lineno">112</tt>  <tt class="py-line"><tt class="py-docstring">          This method returns a tuple ``(x, e)``, where ``x`` is the updated</tt> </tt>
<a name="L113"></a><tt class="py-lineno">113</tt>  <tt class="py-line"><tt class="py-docstring">          estimate of the minimum, and ``e`` is the estimated error.</tt> </tt>
<a name="L114"></a><tt class="py-lineno">114</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L115"></a><tt class="py-lineno">115</tt>  <tt class="py-line">        <tt class="py-name">f</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__f</tt> </tt>
<a name="L116"></a><tt class="py-lineno">116</tt>  <tt class="py-line">        <tt id="link-10" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-10', 'x', 'link-7');">x</a></tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt> </tt>
<a name="L117"></a><tt class="py-lineno">117</tt>  <tt class="py-line">        <tt class="py-name">fo</tt> <tt class="py-op">=</tt> <tt class="py-name">f</tt><tt class="py-op">(</tt><tt id="link-11" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-11', 'x', 'link-7');">x</a></tt><tt class="py-op">)</tt> </tt>
<a name="L118"></a><tt class="py-lineno">118</tt>  <tt class="py-line"> </tt>
<a name="L119"></a><tt class="py-lineno">119</tt>  <tt class="py-line">        <tt class="py-comment"># Computes next estimate</tt> </tt>
<a name="L120"></a><tt class="py-lineno">120</tt>  <tt class="py-line">        <tt id="link-12" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-12', 'x', 'link-7');">x</a></tt> <tt class="py-op">=</tt> <tt id="link-13" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-13', 'x', 'link-7');">x</a></tt> <tt class="py-op">+</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__h</tt> </tt>
<a name="L121"></a><tt class="py-lineno">121</tt>  <tt class="py-line"> </tt>
<a name="L122"></a><tt class="py-lineno">122</tt>  <tt class="py-line">         <tt class="py-comment"># Sanity check</tt> </tt>
<a name="L123"></a><tt class="py-lineno">123</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">range</tt> <tt class="py-keyword">is</tt> <tt class="py-keyword">not</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> </tt>
<a name="L124"></a><tt class="py-lineno">124</tt>  <tt class="py-line">            <tt class="py-name">r0</tt><tt class="py-op">,</tt> <tt class="py-name">r1</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">range</tt> </tt>
<a name="L125"></a><tt class="py-lineno">125</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt id="link-14" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-14', 'x', 'link-7');">x</a></tt> <tt class="py-op">&lt;</tt> <tt class="py-name">r0</tt><tt class="py-op">:</tt> <tt id="link-15" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-15', 'x', 'link-7');">x</a></tt> <tt class="py-op">=</tt> <tt class="py-name">r0</tt> </tt>
<a name="L126"></a><tt class="py-lineno">126</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt id="link-16" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-16', 'x', 'link-7');">x</a></tt> <tt class="py-op">&gt;</tt> <tt class="py-name">r1</tt><tt class="py-op">:</tt> <tt id="link-17" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-17', 'x', 'link-7');">x</a></tt> <tt class="py-op">=</tt> <tt class="py-name">r1</tt> </tt>
<a name="L127"></a><tt class="py-lineno">127</tt>  <tt class="py-line"> </tt>
<a name="L128"></a><tt class="py-lineno">128</tt>  <tt class="py-line">        <tt class="py-comment"># Update state</tt> </tt>
<a name="L129"></a><tt class="py-lineno">129</tt>  <tt class="py-line">        <tt class="py-name">fn</tt> <tt class="py-op">=</tt> <tt class="py-name">f</tt><tt class="py-op">(</tt><tt id="link-18" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-18', 'x', 'link-7');">x</a></tt><tt class="py-op">)</tt> </tt>
<a name="L130"></a><tt class="py-lineno">130</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">fn</tt> <tt class="py-op">&gt;</tt> <tt class="py-name">fo</tt><tt class="py-op">:</tt> </tt>
<a name="L131"></a><tt class="py-lineno">131</tt>  <tt class="py-line">            <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__h</tt> <tt class="py-op">=</tt> <tt class="py-op">-</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__h</tt> <tt class="py-op">/</tt> <tt class="py-number">2.</tt> </tt>
<a name="L132"></a><tt class="py-lineno">132</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt> <tt class="py-op">=</tt> <tt id="link-19" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-19', 'x', 'link-7');">x</a></tt> </tt>
<a name="L133"></a><tt class="py-lineno">133</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-20" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-20', 'x', 'link-7');">x</a></tt><tt class="py-op">,</tt> <tt id="link-21" class="py-name"><a title="peach.nn.rbfn.abs
peach.pso.base.abs" class="py-name" href="#" onclick="return doclink('link-21', 'abs', 'link-1');">abs</a></tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__h</tt><tt class="py-op">)</tt> </tt>
</div><a name="L134"></a><tt class="py-lineno">134</tt>  <tt class="py-line"> </tt>
<a name="L135"></a><tt class="py-lineno">135</tt>  <tt class="py-line"> </tt>
<a name="Direct1D.__call__"></a><div id="Direct1D.__call__-def"><a name="L136"></a><tt class="py-lineno">136</tt> <a class="py-toggle" href="#" id="Direct1D.__call__-toggle" onclick="return toggle('Direct1D.__call__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="peach.optm.linear.Direct1D-class.html#__call__">__call__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Direct1D.__call__-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Direct1D.__call__-expanded"><a name="L137"></a><tt class="py-lineno">137</tt>  <tt class="py-line">        <tt class="py-docstring">'''</tt> </tt>
<a name="L138"></a><tt class="py-lineno">138</tt>  <tt class="py-line"><tt class="py-docstring">        Transparently executes the search until the minimum is found. The stop</tt> </tt>
<a name="L139"></a><tt class="py-lineno">139</tt>  <tt class="py-line"><tt class="py-docstring">        criteria are the maximum error or the maximum number of iterations,</tt> </tt>
<a name="L140"></a><tt class="py-lineno">140</tt>  <tt class="py-line"><tt class="py-docstring">        whichever is reached first. Note that this is a ``__call__`` method, so</tt> </tt>
<a name="L141"></a><tt class="py-lineno">141</tt>  <tt class="py-line"><tt class="py-docstring">        the object is called as a function. This method returns a tuple</tt> </tt>
<a name="L142"></a><tt class="py-lineno">142</tt>  <tt class="py-line"><tt class="py-docstring">        ``(x, e)``, with the best estimate of the minimum and the error.</tt> </tt>
<a name="L143"></a><tt class="py-lineno">143</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L144"></a><tt class="py-lineno">144</tt>  <tt class="py-line"><tt class="py-docstring">        :Returns:</tt> </tt>
<a name="L145"></a><tt class="py-lineno">145</tt>  <tt class="py-line"><tt class="py-docstring">          This method returns a tuple ``(x, e)``, where ``x`` is the best</tt> </tt>
<a name="L146"></a><tt class="py-lineno">146</tt>  <tt class="py-line"><tt class="py-docstring">          estimate of the minimum, and ``e`` is the estimated error.</tt> </tt>
<a name="L147"></a><tt class="py-lineno">147</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L148"></a><tt class="py-lineno">148</tt>  <tt class="py-line">        <tt class="py-name">emax</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__emax</tt> </tt>
<a name="L149"></a><tt class="py-lineno">149</tt>  <tt class="py-line">        <tt class="py-name">imax</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__imax</tt> </tt>
<a name="L150"></a><tt class="py-lineno">150</tt>  <tt class="py-line">        <tt class="py-name">i</tt> <tt class="py-op">=</tt> <tt class="py-number">0</tt> </tt>
<a name="L151"></a><tt class="py-lineno">151</tt>  <tt class="py-line">        <tt class="py-keyword">while</tt> <tt id="link-22" class="py-name"><a title="peach.nn.rbfn.abs
peach.pso.base.abs" class="py-name" href="#" onclick="return doclink('link-22', 'abs', 'link-1');">abs</a></tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__h</tt><tt class="py-op">)</tt> <tt class="py-op">&gt;</tt> <tt class="py-name">emax</tt><tt class="py-op">/</tt><tt class="py-number">2.</tt> <tt class="py-keyword">and</tt> <tt class="py-name">i</tt> <tt class="py-op">&lt;</tt> <tt class="py-name">imax</tt><tt class="py-op">:</tt> </tt>
<a name="L152"></a><tt class="py-lineno">152</tt>  <tt class="py-line">            <tt class="py-name">_</tt><tt class="py-op">,</tt> <tt class="py-name">e</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-23" class="py-name" targets="Method peach.fuzzy.cmeans.FuzzyCMeans.step()=peach.fuzzy.cmeans.FuzzyCMeans-class.html#step,Method peach.ga.base.GeneticAlgorithm.step()=peach.ga.base.GeneticAlgorithm-class.html#step,Method peach.nn.kmeans.KMeans.step()=peach.nn.kmeans.KMeans-class.html#step,Method peach.nn.mem.Hopfield.step()=peach.nn.mem.Hopfield-class.html#step,Method peach.optm.base.Optimizer.step()=peach.optm.base.Optimizer-class.html#step,Method peach.optm.linear.Direct1D.step()=peach.optm.linear.Direct1D-class.html#step,Method peach.optm.linear.Fibonacci.step()=peach.optm.linear.Fibonacci-class.html#step,Method peach.optm.linear.GoldenRule.step()=peach.optm.linear.GoldenRule-class.html#step,Method peach.optm.linear.Interpolation.step()=peach.optm.linear.Interpolation-class.html#step,Method peach.optm.multivar.Direct.step()=peach.optm.multivar.Direct-class.html#step,Method peach.optm.multivar.Gradient.step()=peach.optm.multivar.Gradient-class.html#step,Method peach.optm.multivar.MomentumGradient.step()=peach.optm.multivar.MomentumGradient-class.html#step,Method peach.optm.multivar.Newton.step()=peach.optm.multivar.Newton-class.html#step,Method peach.optm.quasinewton.BFGS.step()=peach.optm.quasinewton.BFGS-class.html#step,Method peach.optm.quasinewton.DFP.step()=peach.optm.quasinewton.DFP-class.html#step,Method peach.optm.quasinewton.SR1.step()=peach.optm.quasinewton.SR1-class.html#step,Method peach.optm.stochastic.CrossEntropy.step()=peach.optm.stochastic.CrossEntropy-class.html#step,Method peach.pso.base.ParticleSwarmOptimizer.step()=peach.pso.base.ParticleSwarmOptimizer-class.html#step,Method peach.sa.base.BinarySA.step()=peach.sa.base.BinarySA-class.html#step,Method peach.sa.base.ContinuousSA.step()=peach.sa.base.ContinuousSA-class.html#step"><a title="peach.fuzzy.cmeans.FuzzyCMeans.step
peach.ga.base.GeneticAlgorithm.step
peach.nn.kmeans.KMeans.step
peach.nn.mem.Hopfield.step
peach.optm.base.Optimizer.step
peach.optm.linear.Direct1D.step
peach.optm.linear.Fibonacci.step
peach.optm.linear.GoldenRule.step
peach.optm.linear.Interpolation.step
peach.optm.multivar.Direct.step
peach.optm.multivar.Gradient.step
peach.optm.multivar.MomentumGradient.step
peach.optm.multivar.Newton.step
peach.optm.quasinewton.BFGS.step
peach.optm.quasinewton.DFP.step
peach.optm.quasinewton.SR1.step
peach.optm.stochastic.CrossEntropy.step
peach.pso.base.ParticleSwarmOptimizer.step
peach.sa.base.BinarySA.step
peach.sa.base.ContinuousSA.step" class="py-name" href="#" onclick="return doclink('link-23', 'step', 'link-23');">step</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L153"></a><tt class="py-lineno">153</tt>  <tt class="py-line">            <tt class="py-name">i</tt> <tt class="py-op">=</tt> <tt class="py-name">i</tt> <tt class="py-op">+</tt> <tt class="py-number">1</tt> </tt>
<a name="L154"></a><tt class="py-lineno">154</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt><tt class="py-op">,</tt> <tt class="py-name">e</tt> </tt>
</div></div><a name="L155"></a><tt class="py-lineno">155</tt>  <tt class="py-line"> </tt>
<a name="L156"></a><tt class="py-lineno">156</tt>  <tt class="py-line"> </tt>
<a name="L157"></a><tt class="py-lineno">157</tt>  <tt class="py-line"><tt class="py-comment">################################################################################</tt> </tt>
<a name="Interpolation"></a><div id="Interpolation-def"><a name="L158"></a><tt class="py-lineno">158</tt> <a class="py-toggle" href="#" id="Interpolation-toggle" onclick="return toggle('Interpolation');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="peach.optm.linear.Interpolation-class.html">Interpolation</a><tt class="py-op">(</tt><tt class="py-base-class">Optimizer</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Interpolation-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="Interpolation-expanded"><a name="L159"></a><tt class="py-lineno">159</tt>  <tt class="py-line">    <tt class="py-docstring">'''</tt> </tt>
<a name="L160"></a><tt class="py-lineno">160</tt>  <tt class="py-line"><tt class="py-docstring">    Optimization by quadractic interpolation.</tt> </tt>
<a name="L161"></a><tt class="py-lineno">161</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L162"></a><tt class="py-lineno">162</tt>  <tt class="py-line"><tt class="py-docstring">    This methods takes three estimates and finds the parabolic function that</tt> </tt>
<a name="L163"></a><tt class="py-lineno">163</tt>  <tt class="py-line"><tt class="py-docstring">    fits them, and returns as a new estimate the vertex of the parabola. The</tt> </tt>
<a name="L164"></a><tt class="py-lineno">164</tt>  <tt class="py-line"><tt class="py-docstring">    procedure can be repeated until a good approximation is found.</tt> </tt>
<a name="L165"></a><tt class="py-lineno">165</tt>  <tt class="py-line"><tt class="py-docstring">    '''</tt> </tt>
<a name="Interpolation.__init__"></a><div id="Interpolation.__init__-def"><a name="L166"></a><tt class="py-lineno">166</tt> <a class="py-toggle" href="#" id="Interpolation.__init__-toggle" onclick="return toggle('Interpolation.__init__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="peach.optm.linear.Interpolation-class.html#__init__">__init__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">f</tt><tt class="py-op">,</tt> <tt class="py-param">x0</tt><tt class="py-op">,</tt> <tt class="py-param">emax</tt><tt class="py-op">=</tt><tt class="py-number">1e-8</tt><tt class="py-op">,</tt> <tt class="py-param">imax</tt><tt class="py-op">=</tt><tt class="py-number">1000</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Interpolation.__init__-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Interpolation.__init__-expanded"><a name="L167"></a><tt class="py-lineno">167</tt>  <tt class="py-line">        <tt class="py-docstring">'''</tt> </tt>
<a name="L168"></a><tt class="py-lineno">168</tt>  <tt class="py-line"><tt class="py-docstring">        Initializes the optimizer.</tt> </tt>
<a name="L169"></a><tt class="py-lineno">169</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L170"></a><tt class="py-lineno">170</tt>  <tt class="py-line"><tt class="py-docstring">        To create an optimizer of this type, instantiate the class with the</tt> </tt>
<a name="L171"></a><tt class="py-lineno">171</tt>  <tt class="py-line"><tt class="py-docstring">        parameters given below:</tt> </tt>
<a name="L172"></a><tt class="py-lineno">172</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L173"></a><tt class="py-lineno">173</tt>  <tt class="py-line"><tt class="py-docstring">        :Parameters:</tt> </tt>
<a name="L174"></a><tt class="py-lineno">174</tt>  <tt class="py-line"><tt class="py-docstring">          f</tt> </tt>
<a name="L175"></a><tt class="py-lineno">175</tt>  <tt class="py-line"><tt class="py-docstring">            A one variable only function to be optimized. The function should</tt> </tt>
<a name="L176"></a><tt class="py-lineno">176</tt>  <tt class="py-line"><tt class="py-docstring">            have only one parameter and return the function value.</tt> </tt>
<a name="L177"></a><tt class="py-lineno">177</tt>  <tt class="py-line"><tt class="py-docstring">          x0</tt> </tt>
<a name="L178"></a><tt class="py-lineno">178</tt>  <tt class="py-line"><tt class="py-docstring">            First estimate of the minimum. The interpolation search needs three</tt> </tt>
<a name="L179"></a><tt class="py-lineno">179</tt>  <tt class="py-line"><tt class="py-docstring">            estimates to approximate the parabolic function. Thus, the first</tt> </tt>
<a name="L180"></a><tt class="py-lineno">180</tt>  <tt class="py-line"><tt class="py-docstring">            estimate must be a triple ``(xl, xm, xh)``, with the property that</tt> </tt>
<a name="L181"></a><tt class="py-lineno">181</tt>  <tt class="py-line"><tt class="py-docstring">            ``xl &lt; xm &lt; xh``. Be aware, however, that no checking is done -- if</tt> </tt>
<a name="L182"></a><tt class="py-lineno">182</tt>  <tt class="py-line"><tt class="py-docstring">            the estimate doesn't correspond to this condition, in some point an</tt> </tt>
<a name="L183"></a><tt class="py-lineno">183</tt>  <tt class="py-line"><tt class="py-docstring">            exception will be raised.</tt> </tt>
<a name="L184"></a><tt class="py-lineno">184</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L185"></a><tt class="py-lineno">185</tt>  <tt class="py-line"><tt class="py-docstring">            Notice that, given the nature of the estimate of the interpolation</tt> </tt>
<a name="L186"></a><tt class="py-lineno">186</tt>  <tt class="py-line"><tt class="py-docstring">            method, it is not necessary to have a specific parameter to restrict</tt> </tt>
<a name="L187"></a><tt class="py-lineno">187</tt>  <tt class="py-line"><tt class="py-docstring">            the range of acceptable values -- it is already embedded in the</tt> </tt>
<a name="L188"></a><tt class="py-lineno">188</tt>  <tt class="py-line"><tt class="py-docstring">            estimate. If you need to restrict your estimate between an interval,</tt> </tt>
<a name="L189"></a><tt class="py-lineno">189</tt>  <tt class="py-line"><tt class="py-docstring">            just use its limits as ``xl`` and ``xh`` in the estimate.</tt> </tt>
<a name="L190"></a><tt class="py-lineno">190</tt>  <tt class="py-line"><tt class="py-docstring">          emax</tt> </tt>
<a name="L191"></a><tt class="py-lineno">191</tt>  <tt class="py-line"><tt class="py-docstring">            Maximum allowed error. The algorithm stops as soon as the error is</tt> </tt>
<a name="L192"></a><tt class="py-lineno">192</tt>  <tt class="py-line"><tt class="py-docstring">            below this level. The error is absolute.</tt> </tt>
<a name="L193"></a><tt class="py-lineno">193</tt>  <tt class="py-line"><tt class="py-docstring">          imax</tt> </tt>
<a name="L194"></a><tt class="py-lineno">194</tt>  <tt class="py-line"><tt class="py-docstring">            Maximum number of iterations, the algorithm stops as soon this</tt> </tt>
<a name="L195"></a><tt class="py-lineno">195</tt>  <tt class="py-line"><tt class="py-docstring">            number of iterations are executed, no matter what the error is at</tt> </tt>
<a name="L196"></a><tt class="py-lineno">196</tt>  <tt class="py-line"><tt class="py-docstring">            the moment.</tt> </tt>
<a name="L197"></a><tt class="py-lineno">197</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L198"></a><tt class="py-lineno">198</tt>  <tt class="py-line">        <tt id="link-24" class="py-name"><a title="peach.optm.base.Optimizer" class="py-name" href="#" onclick="return doclink('link-24', 'Optimizer', 'link-3');">Optimizer</a></tt><tt class="py-op">.</tt><tt id="link-25" class="py-name"><a title="peach.fuzzy.base.FuzzySet.__init__
peach.fuzzy.cmeans.FuzzyCMeans.__init__
peach.fuzzy.control.Controller.__init__
peach.fuzzy.control.Parametric.__init__
peach.fuzzy.mf.Bell.__init__
peach.fuzzy.mf.DecreasingRamp.__init__
peach.fuzzy.mf.DecreasingSigmoid.__init__
peach.fuzzy.mf.Gaussian.__init__
peach.fuzzy.mf.IncreasingRamp.__init__
peach.fuzzy.mf.IncreasingSigmoid.__init__
peach.fuzzy.mf.Membership.__init__
peach.fuzzy.mf.RaisedCosine.__init__
peach.fuzzy.mf.Smf.__init__
peach.fuzzy.mf.Trapezoid.__init__
peach.fuzzy.mf.Triangle.__init__
peach.fuzzy.mf.Zmf.__init__
peach.ga.base.GeneticAlgorithm.__init__
peach.ga.chromosome.Chromosome.__init__
peach.ga.crossover.OnePoint.__init__
peach.ga.crossover.TwoPoint.__init__
peach.ga.crossover.Uniform.__init__
peach.ga.fitness.Fitness.__init__
peach.ga.fitness.Ranking.__init__
peach.ga.mutation.BitToBit.__init__
peach.nn.af.Activation.__init__
peach.nn.af.ArcTan.__init__
peach.nn.af.Gaussian.__init__
peach.nn.af.Linear.__init__
peach.nn.af.Ramp.__init__
peach.nn.af.Sigmoid.__init__
peach.nn.af.Signum.__init__
peach.nn.af.TanH.__init__
peach.nn.af.Threshold.__init__
peach.nn.base.Layer.__init__
peach.nn.kmeans.KMeans.__init__
peach.nn.lrules.BackPropagation.__init__
peach.nn.lrules.Competitive.__init__
peach.nn.lrules.Cooperative.__init__
peach.nn.lrules.LMS.__init__
peach.nn.lrules.WinnerTakesAll.__init__
peach.nn.mem.Hopfield.__init__
peach.nn.nnet.FeedForward.__init__
peach.nn.nnet.GRNN.__init__
peach.nn.nnet.PNN.__init__
peach.nn.nnet.SOM.__init__
peach.nn.rbfn.RBFN.__init__
peach.optm.base.Optimizer.__init__
peach.optm.linear.Direct1D.__init__
peach.optm.linear.Fibonacci.__init__
peach.optm.linear.GoldenRule.__init__
peach.optm.linear.Interpolation.__init__
peach.optm.multivar.Direct.__init__
peach.optm.multivar.Gradient.__init__
peach.optm.multivar.MomentumGradient.__init__
peach.optm.multivar.Newton.__init__
peach.optm.quasinewton.BFGS.__init__
peach.optm.quasinewton.DFP.__init__
peach.optm.quasinewton.SR1.__init__
peach.optm.stochastic.CrossEntropy.__init__
peach.pso.acc.Accelerator.__init__
peach.pso.acc.StandardPSO.__init__
peach.pso.base.ParticleSwarmOptimizer.__init__
peach.sa.base.BinarySA.__init__
peach.sa.base.ContinuousSA.__init__
peach.sa.neighbor.BinaryNeighbor.__init__
peach.sa.neighbor.ContinuousNeighbor.__init__
peach.sa.neighbor.GaussianNeighbor.__init__
peach.sa.neighbor.InvertBitsNeighbor.__init__
peach.sa.neighbor.UniformNeighbor.__init__" class="py-name" href="#" onclick="return doclink('link-25', '__init__', 'link-5');">__init__</a></tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">)</tt> </tt>
<a name="L199"></a><tt class="py-lineno">199</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__f</tt> <tt class="py-op">=</tt> <tt class="py-name">f</tt> </tt>
<a name="L200"></a><tt class="py-lineno">200</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt> <tt class="py-op">=</tt> <tt class="py-name">x0</tt> </tt>
<a name="L201"></a><tt class="py-lineno">201</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__emax</tt> <tt class="py-op">=</tt> <tt class="py-name">float</tt><tt class="py-op">(</tt><tt class="py-name">emax</tt><tt class="py-op">)</tt> </tt>
<a name="L202"></a><tt class="py-lineno">202</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__imax</tt> <tt class="py-op">=</tt> <tt class="py-name">int</tt><tt class="py-op">(</tt><tt class="py-name">imax</tt><tt class="py-op">)</tt> </tt>
</div><a name="L203"></a><tt class="py-lineno">203</tt>  <tt class="py-line"> </tt>
<a name="L204"></a><tt class="py-lineno">204</tt>  <tt class="py-line"> </tt>
<a name="Interpolation.__get_x"></a><div id="Interpolation.__get_x-def"><a name="L205"></a><tt class="py-lineno">205</tt> <a class="py-toggle" href="#" id="Interpolation.__get_x-toggle" onclick="return toggle('Interpolation.__get_x');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="peach.optm.linear.Interpolation-class.html#__get_x">__get_x</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Interpolation.__get_x-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Interpolation.__get_x-expanded"><a name="L206"></a><tt class="py-lineno">206</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt> </tt>
</div><a name="L207"></a><tt class="py-lineno">207</tt>  <tt class="py-line"> </tt>
<a name="Interpolation.__set_x"></a><div id="Interpolation.__set_x-def"><a name="L208"></a><tt class="py-lineno">208</tt> <a class="py-toggle" href="#" id="Interpolation.__set_x-toggle" onclick="return toggle('Interpolation.__set_x');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="peach.optm.linear.Interpolation-class.html#__set_x">__set_x</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x0</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Interpolation.__set_x-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Interpolation.__set_x-expanded"><a name="L209"></a><tt class="py-lineno">209</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-26" class="py-name"><a title="peach.ga.base.GeneticAlgorithm.restart
peach.optm.linear.Direct1D.restart
peach.optm.linear.Fibonacci.restart
peach.optm.linear.GoldenRule.restart
peach.optm.linear.Interpolation.restart
peach.optm.multivar.Direct.restart
peach.optm.multivar.Gradient.restart
peach.optm.multivar.MomentumGradient.restart
peach.optm.multivar.Newton.restart
peach.optm.quasinewton.BFGS.restart
peach.optm.quasinewton.DFP.restart
peach.optm.quasinewton.SR1.restart
peach.pso.base.ParticleSwarmOptimizer.restart
peach.sa.base.BinarySA.restart
peach.sa.base.ContinuousSA.restart" class="py-name" href="#" onclick="return doclink('link-26', 'restart', 'link-6');">restart</a></tt><tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">)</tt> </tt>
</div><a name="L210"></a><tt class="py-lineno">210</tt>  <tt class="py-line"> </tt>
<a name="L211"></a><tt class="py-lineno">211</tt>  <tt class="py-line">    <tt id="link-27" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-27', 'x', 'link-7');">x</a></tt> <tt class="py-op">=</tt> <tt class="py-name">property</tt><tt class="py-op">(</tt><tt id="link-28" class="py-name"><a title="peach.optm.linear.Direct1D.__get_x
peach.optm.linear.GoldenRule.__get_x
peach.optm.linear.Interpolation.__get_x
peach.optm.multivar.Direct.__get_x
peach.optm.multivar.Gradient.__get_x
peach.optm.multivar.MomentumGradient.__get_x
peach.optm.multivar.Newton.__get_x
peach.optm.quasinewton.DFP.__get_x
peach.optm.quasinewton.SR1.__get_x
peach.sa.base.BinarySA.__get_x
peach.sa.base.ContinuousSA.__get_x" class="py-name" href="#" onclick="return doclink('link-28', '__get_x', 'link-8');">__get_x</a></tt><tt class="py-op">,</tt> <tt id="link-29" class="py-name"><a title="peach.optm.linear.Direct1D.__set_x
peach.optm.linear.GoldenRule.__set_x
peach.optm.linear.Interpolation.__set_x
peach.optm.multivar.Direct.__set_x
peach.optm.multivar.Gradient.__set_x
peach.optm.multivar.MomentumGradient.__set_x
peach.optm.multivar.Newton.__set_x
peach.optm.quasinewton.DFP.__set_x
peach.optm.quasinewton.SR1.__set_x
peach.sa.base.BinarySA.__set_x
peach.sa.base.ContinuousSA.__set_x" class="py-name" href="#" onclick="return doclink('link-29', '__set_x', 'link-9');">__set_x</a></tt><tt class="py-op">)</tt> </tt>
<a name="L212"></a><tt class="py-lineno">212</tt>  <tt class="py-line">    <tt class="py-string">'''The estimate of the position of the minimum.'''</tt> </tt>
<a name="L213"></a><tt class="py-lineno">213</tt>  <tt class="py-line"> </tt>
<a name="L214"></a><tt class="py-lineno">214</tt>  <tt class="py-line"> </tt>
<a name="Interpolation.restart"></a><div id="Interpolation.restart-def"><a name="L215"></a><tt class="py-lineno">215</tt> <a class="py-toggle" href="#" id="Interpolation.restart-toggle" onclick="return toggle('Interpolation.restart');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="peach.optm.linear.Interpolation-class.html#restart">restart</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x0</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Interpolation.restart-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Interpolation.restart-expanded"><a name="L216"></a><tt class="py-lineno">216</tt>  <tt class="py-line">        <tt class="py-docstring">'''</tt> </tt>
<a name="L217"></a><tt class="py-lineno">217</tt>  <tt class="py-line"><tt class="py-docstring">        Resets the optimizer, returning to its original state, and allowing to</tt> </tt>
<a name="L218"></a><tt class="py-lineno">218</tt>  <tt class="py-line"><tt class="py-docstring">        use a new first estimate.</tt> </tt>
<a name="L219"></a><tt class="py-lineno">219</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L220"></a><tt class="py-lineno">220</tt>  <tt class="py-line"><tt class="py-docstring">        :Parameters:</tt> </tt>
<a name="L221"></a><tt class="py-lineno">221</tt>  <tt class="py-line"><tt class="py-docstring">          x0</tt> </tt>
<a name="L222"></a><tt class="py-lineno">222</tt>  <tt class="py-line"><tt class="py-docstring">            The new initial value of the estimate of the minimum. The</tt> </tt>
<a name="L223"></a><tt class="py-lineno">223</tt>  <tt class="py-line"><tt class="py-docstring">            interpolation search needs three estimates to approximate the</tt> </tt>
<a name="L224"></a><tt class="py-lineno">224</tt>  <tt class="py-line"><tt class="py-docstring">            parabolic function. Thus, the estimate must be a triple</tt> </tt>
<a name="L225"></a><tt class="py-lineno">225</tt>  <tt class="py-line"><tt class="py-docstring">            ``(xl, xm, xh)``, with the property that ``xl &lt; xm &lt; xh``. Be aware,</tt> </tt>
<a name="L226"></a><tt class="py-lineno">226</tt>  <tt class="py-line"><tt class="py-docstring">            however, that no checking is done -- if the estimate doesn't</tt> </tt>
<a name="L227"></a><tt class="py-lineno">227</tt>  <tt class="py-line"><tt class="py-docstring">            correspond to this condition, in some point an exception will be</tt> </tt>
<a name="L228"></a><tt class="py-lineno">228</tt>  <tt class="py-line"><tt class="py-docstring">            raised.</tt> </tt>
<a name="L229"></a><tt class="py-lineno">229</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L230"></a><tt class="py-lineno">230</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt> <tt class="py-op">=</tt> <tt class="py-name">x0</tt> </tt>
</div><a name="L231"></a><tt class="py-lineno">231</tt>  <tt class="py-line"> </tt>
<a name="L232"></a><tt class="py-lineno">232</tt>  <tt class="py-line"> </tt>
<a name="Interpolation.step"></a><div id="Interpolation.step-def"><a name="L233"></a><tt class="py-lineno">233</tt> <a class="py-toggle" href="#" id="Interpolation.step-toggle" onclick="return toggle('Interpolation.step');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="peach.optm.linear.Interpolation-class.html#step">step</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Interpolation.step-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Interpolation.step-expanded"><a name="L234"></a><tt class="py-lineno">234</tt>  <tt class="py-line">        <tt class="py-docstring">'''</tt> </tt>
<a name="L235"></a><tt class="py-lineno">235</tt>  <tt class="py-line"><tt class="py-docstring">        One step of the search.</tt> </tt>
<a name="L236"></a><tt class="py-lineno">236</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L237"></a><tt class="py-lineno">237</tt>  <tt class="py-line"><tt class="py-docstring">        In this method, the result of the step is dependent only of the given</tt> </tt>
<a name="L238"></a><tt class="py-lineno">238</tt>  <tt class="py-line"><tt class="py-docstring">        estimated, so it can be used for different kind of investigations on the</tt> </tt>
<a name="L239"></a><tt class="py-lineno">239</tt>  <tt class="py-line"><tt class="py-docstring">        same cost function.</tt> </tt>
<a name="L240"></a><tt class="py-lineno">240</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L241"></a><tt class="py-lineno">241</tt>  <tt class="py-line"><tt class="py-docstring">        :Returns:</tt> </tt>
<a name="L242"></a><tt class="py-lineno">242</tt>  <tt class="py-line"><tt class="py-docstring">          This method returns a tuple ``(x, e)``, where ``x`` is the updated</tt> </tt>
<a name="L243"></a><tt class="py-lineno">243</tt>  <tt class="py-line"><tt class="py-docstring">          triplet of estimates of the minimum, and ``e`` is the estimated error.</tt> </tt>
<a name="L244"></a><tt class="py-lineno">244</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L245"></a><tt class="py-lineno">245</tt>  <tt class="py-line">        <tt class="py-name">x0</tt><tt class="py-op">,</tt> <tt class="py-name">x1</tt><tt class="py-op">,</tt> <tt class="py-name">x2</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt> </tt>
<a name="L246"></a><tt class="py-lineno">246</tt>  <tt class="py-line">        <tt class="py-name">f</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__f</tt> </tt>
<a name="L247"></a><tt class="py-lineno">247</tt>  <tt class="py-line">        <tt class="py-name">q0</tt> <tt class="py-op">=</tt> <tt class="py-name">x0</tt> <tt class="py-op">*</tt> <tt class="py-op">(</tt><tt class="py-name">f</tt><tt class="py-op">(</tt><tt class="py-name">x1</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-name">f</tt><tt class="py-op">(</tt><tt class="py-name">x2</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L248"></a><tt class="py-lineno">248</tt>  <tt class="py-line">        <tt class="py-name">q1</tt> <tt class="py-op">=</tt> <tt class="py-name">x1</tt> <tt class="py-op">*</tt> <tt class="py-op">(</tt><tt class="py-name">f</tt><tt class="py-op">(</tt><tt class="py-name">x2</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-name">f</tt><tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L249"></a><tt class="py-lineno">249</tt>  <tt class="py-line">        <tt class="py-name">q2</tt> <tt class="py-op">=</tt> <tt class="py-name">x2</tt> <tt class="py-op">*</tt> <tt class="py-op">(</tt><tt class="py-name">f</tt><tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-name">f</tt><tt class="py-op">(</tt><tt class="py-name">x1</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L250"></a><tt class="py-lineno">250</tt>  <tt class="py-line">        <tt class="py-name">q</tt> <tt class="py-op">=</tt> <tt class="py-name">q0</tt> <tt class="py-op">+</tt> <tt class="py-name">q1</tt> <tt class="py-op">+</tt> <tt class="py-name">q2</tt> </tt>
<a name="L251"></a><tt class="py-lineno">251</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">q</tt> <tt class="py-op">==</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L252"></a><tt class="py-lineno">252</tt>  <tt class="py-line">            <tt class="py-keyword">return</tt> <tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">,</tt> <tt class="py-name">x1</tt><tt class="py-op">,</tt> <tt class="py-name">x2</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">max</tt><tt class="py-op">(</tt><tt id="link-30" class="py-name"><a title="peach.nn.rbfn.abs
peach.pso.base.abs" class="py-name" href="#" onclick="return doclink('link-30', 'abs', 'link-1');">abs</a></tt><tt class="py-op">(</tt><tt class="py-name">x1</tt><tt class="py-op">-</tt><tt class="py-name">x0</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt id="link-31" class="py-name"><a title="peach.nn.rbfn.abs
peach.pso.base.abs" class="py-name" href="#" onclick="return doclink('link-31', 'abs', 'link-1');">abs</a></tt><tt class="py-op">(</tt><tt class="py-name">x2</tt><tt class="py-op">-</tt><tt class="py-name">x1</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L253"></a><tt class="py-lineno">253</tt>  <tt class="py-line">        <tt class="py-name">xm</tt> <tt class="py-op">=</tt> <tt class="py-number">0.5</tt> <tt class="py-op">*</tt> <tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">*</tt><tt class="py-name">q0</tt> <tt class="py-op">+</tt> <tt class="py-name">x1</tt><tt class="py-op">*</tt><tt class="py-name">q1</tt> <tt class="py-op">+</tt> <tt class="py-name">x2</tt><tt class="py-op">*</tt><tt class="py-name">q2</tt><tt class="py-op">)</tt> <tt class="py-op">/</tt> <tt class="py-op">(</tt><tt class="py-name">q0</tt> <tt class="py-op">+</tt> <tt class="py-name">q1</tt> <tt class="py-op">+</tt> <tt class="py-name">q2</tt><tt class="py-op">)</tt> </tt>
<a name="L254"></a><tt class="py-lineno">254</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">xm</tt> <tt class="py-op">&lt;</tt> <tt class="py-name">x0</tt><tt class="py-op">:</tt> </tt>
<a name="L255"></a><tt class="py-lineno">255</tt>  <tt class="py-line">            <tt id="link-32" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-32', 'x', 'link-7');">x</a></tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">xm</tt><tt class="py-op">,</tt> <tt class="py-name">x0</tt><tt class="py-op">,</tt> <tt class="py-name">x1</tt><tt class="py-op">)</tt> </tt>
<a name="L256"></a><tt class="py-lineno">256</tt>  <tt class="py-line">        <tt class="py-keyword">elif</tt> <tt class="py-name">x0</tt> <tt class="py-op">&lt;</tt> <tt class="py-name">xm</tt> <tt class="py-op">&lt;</tt> <tt class="py-name">x1</tt><tt class="py-op">:</tt> </tt>
<a name="L257"></a><tt class="py-lineno">257</tt>  <tt class="py-line">            <tt id="link-33" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-33', 'x', 'link-7');">x</a></tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">,</tt> <tt class="py-name">xm</tt><tt class="py-op">,</tt> <tt class="py-name">x1</tt><tt class="py-op">)</tt> </tt>
<a name="L258"></a><tt class="py-lineno">258</tt>  <tt class="py-line">        <tt class="py-keyword">elif</tt> <tt class="py-name">x1</tt> <tt class="py-op">&lt;</tt> <tt class="py-name">xm</tt> <tt class="py-op">&lt;</tt> <tt class="py-name">x2</tt><tt class="py-op">:</tt> </tt>
<a name="L259"></a><tt class="py-lineno">259</tt>  <tt class="py-line">            <tt id="link-34" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-34', 'x', 'link-7');">x</a></tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">x1</tt><tt class="py-op">,</tt> <tt class="py-name">xm</tt><tt class="py-op">,</tt> <tt class="py-name">x2</tt><tt class="py-op">)</tt> </tt>
<a name="L260"></a><tt class="py-lineno">260</tt>  <tt class="py-line">        <tt class="py-keyword">elif</tt> <tt class="py-name">x2</tt> <tt class="py-op">&lt;</tt> <tt class="py-name">xm</tt><tt class="py-op">:</tt> </tt>
<a name="L261"></a><tt class="py-lineno">261</tt>  <tt class="py-line">            <tt id="link-35" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-35', 'x', 'link-7');">x</a></tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">x1</tt><tt class="py-op">,</tt> <tt class="py-name">x2</tt><tt class="py-op">,</tt>  <tt class="py-name">xm</tt><tt class="py-op">)</tt> </tt>
<a name="L262"></a><tt class="py-lineno">262</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L263"></a><tt class="py-lineno">263</tt>  <tt class="py-line">            <tt id="link-36" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-36', 'x', 'link-7');">x</a></tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">xm</tt><tt class="py-op">,</tt> <tt class="py-name">xm</tt><tt class="py-op">,</tt> <tt class="py-name">xm</tt><tt class="py-op">)</tt> </tt>
<a name="L264"></a><tt class="py-lineno">264</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt> <tt class="py-op">=</tt> <tt id="link-37" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-37', 'x', 'link-7');">x</a></tt> </tt>
<a name="L265"></a><tt class="py-lineno">265</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-38" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-38', 'x', 'link-7');">x</a></tt><tt class="py-op">,</tt> <tt class="py-name">max</tt><tt class="py-op">(</tt><tt id="link-39" class="py-name"><a title="peach.nn.rbfn.abs
peach.pso.base.abs" class="py-name" href="#" onclick="return doclink('link-39', 'abs', 'link-1');">abs</a></tt><tt class="py-op">(</tt><tt class="py-name">xm</tt><tt class="py-op">-</tt><tt class="py-name">x0</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt id="link-40" class="py-name"><a title="peach.nn.rbfn.abs
peach.pso.base.abs" class="py-name" href="#" onclick="return doclink('link-40', 'abs', 'link-1');">abs</a></tt><tt class="py-op">(</tt><tt class="py-name">x2</tt><tt class="py-op">-</tt><tt class="py-name">xm</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
</div><a name="L266"></a><tt class="py-lineno">266</tt>  <tt class="py-line"> </tt>
<a name="L267"></a><tt class="py-lineno">267</tt>  <tt class="py-line"> </tt>
<a name="Interpolation.__call__"></a><div id="Interpolation.__call__-def"><a name="L268"></a><tt class="py-lineno">268</tt> <a class="py-toggle" href="#" id="Interpolation.__call__-toggle" onclick="return toggle('Interpolation.__call__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="peach.optm.linear.Interpolation-class.html#__call__">__call__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Interpolation.__call__-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Interpolation.__call__-expanded"><a name="L269"></a><tt class="py-lineno">269</tt>  <tt class="py-line">        <tt class="py-docstring">'''</tt> </tt>
<a name="L270"></a><tt class="py-lineno">270</tt>  <tt class="py-line"><tt class="py-docstring">        Transparently executes the search until the minimum is found. The stop</tt> </tt>
<a name="L271"></a><tt class="py-lineno">271</tt>  <tt class="py-line"><tt class="py-docstring">        criteria are the maximum error or the maximum number of iterations,</tt> </tt>
<a name="L272"></a><tt class="py-lineno">272</tt>  <tt class="py-line"><tt class="py-docstring">        whichever is reached first. Note that this is a ``__call__`` method, so</tt> </tt>
<a name="L273"></a><tt class="py-lineno">273</tt>  <tt class="py-line"><tt class="py-docstring">        the object is called as a function. This method returns a tuple</tt> </tt>
<a name="L274"></a><tt class="py-lineno">274</tt>  <tt class="py-line"><tt class="py-docstring">        ``(x, e)``, with the best estimate of the minimum and the error.</tt> </tt>
<a name="L275"></a><tt class="py-lineno">275</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L276"></a><tt class="py-lineno">276</tt>  <tt class="py-line"><tt class="py-docstring">        :Returns:</tt> </tt>
<a name="L277"></a><tt class="py-lineno">277</tt>  <tt class="py-line"><tt class="py-docstring">          This method returns a tuple ``(x, e)``, where ``x`` is the best</tt> </tt>
<a name="L278"></a><tt class="py-lineno">278</tt>  <tt class="py-line"><tt class="py-docstring">          estimate of the minimum, and ``e`` is the estimated error.</tt> </tt>
<a name="L279"></a><tt class="py-lineno">279</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L280"></a><tt class="py-lineno">280</tt>  <tt class="py-line">        <tt class="py-name">emax</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__emax</tt> </tt>
<a name="L281"></a><tt class="py-lineno">281</tt>  <tt class="py-line">        <tt class="py-name">imax</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__imax</tt> </tt>
<a name="L282"></a><tt class="py-lineno">282</tt>  <tt class="py-line">        <tt class="py-name">e</tt> <tt class="py-op">=</tt> <tt class="py-name">emax</tt> </tt>
<a name="L283"></a><tt class="py-lineno">283</tt>  <tt class="py-line">        <tt class="py-name">i</tt> <tt class="py-op">=</tt> <tt class="py-number">0</tt> </tt>
<a name="L284"></a><tt class="py-lineno">284</tt>  <tt class="py-line">        <tt class="py-keyword">while</tt> <tt class="py-name">e</tt> <tt class="py-op">&gt;</tt> <tt class="py-name">emax</tt><tt class="py-op">/</tt><tt class="py-number">2.</tt> <tt class="py-keyword">and</tt> <tt class="py-name">i</tt> <tt class="py-op">&lt;</tt> <tt class="py-name">imax</tt><tt class="py-op">:</tt> </tt>
<a name="L285"></a><tt class="py-lineno">285</tt>  <tt class="py-line">            <tt class="py-name">x0</tt><tt class="py-op">,</tt> <tt class="py-name">x1</tt><tt class="py-op">,</tt> <tt class="py-name">x2</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt> </tt>
<a name="L286"></a><tt class="py-lineno">286</tt>  <tt class="py-line">            <tt class="py-name">_</tt><tt class="py-op">,</tt> <tt class="py-name">e</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-41" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.step
peach.ga.base.GeneticAlgorithm.step
peach.nn.kmeans.KMeans.step
peach.nn.mem.Hopfield.step
peach.optm.base.Optimizer.step
peach.optm.linear.Direct1D.step
peach.optm.linear.Fibonacci.step
peach.optm.linear.GoldenRule.step
peach.optm.linear.Interpolation.step
peach.optm.multivar.Direct.step
peach.optm.multivar.Gradient.step
peach.optm.multivar.MomentumGradient.step
peach.optm.multivar.Newton.step
peach.optm.quasinewton.BFGS.step
peach.optm.quasinewton.DFP.step
peach.optm.quasinewton.SR1.step
peach.optm.stochastic.CrossEntropy.step
peach.pso.base.ParticleSwarmOptimizer.step
peach.sa.base.BinarySA.step
peach.sa.base.ContinuousSA.step" class="py-name" href="#" onclick="return doclink('link-41', 'step', 'link-23');">step</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L287"></a><tt class="py-lineno">287</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt class="py-name">x0</tt> <tt class="py-op">==</tt> <tt class="py-name">x1</tt><tt class="py-op">:</tt> </tt>
<a name="L288"></a><tt class="py-lineno">288</tt>  <tt class="py-line">                <tt class="py-keyword">return</tt> <tt class="py-name">x0</tt><tt class="py-op">,</tt> <tt class="py-name">e</tt> </tt>
<a name="L289"></a><tt class="py-lineno">289</tt>  <tt class="py-line">            <tt class="py-keyword">elif</tt> <tt class="py-name">x1</tt> <tt class="py-op">==</tt> <tt class="py-name">x2</tt><tt class="py-op">:</tt> </tt>
<a name="L290"></a><tt class="py-lineno">290</tt>  <tt class="py-line">                <tt class="py-keyword">return</tt> <tt class="py-name">x1</tt><tt class="py-op">,</tt> <tt class="py-name">e</tt> </tt>
<a name="L291"></a><tt class="py-lineno">291</tt>  <tt class="py-line">            <tt class="py-keyword">elif</tt> <tt class="py-name">x0</tt> <tt class="py-op">==</tt> <tt class="py-name">x2</tt><tt class="py-op">:</tt> </tt>
<a name="L292"></a><tt class="py-lineno">292</tt>  <tt class="py-line">                <tt class="py-keyword">return</tt> <tt class="py-name">x2</tt><tt class="py-op">,</tt> <tt class="py-name">e</tt> </tt>
<a name="L293"></a><tt class="py-lineno">293</tt>  <tt class="py-line">            <tt class="py-name">i</tt> <tt class="py-op">=</tt> <tt class="py-name">i</tt> <tt class="py-op">+</tt> <tt class="py-number">1</tt> </tt>
<a name="L294"></a><tt class="py-lineno">294</tt>  <tt class="py-line">        <tt class="py-name">f</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__f</tt> </tt>
<a name="L295"></a><tt class="py-lineno">295</tt>  <tt class="py-line">        <tt class="py-name">q0</tt> <tt class="py-op">=</tt> <tt class="py-name">x0</tt> <tt class="py-op">*</tt> <tt class="py-op">(</tt><tt class="py-name">f</tt><tt class="py-op">(</tt><tt class="py-name">x1</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-name">f</tt><tt class="py-op">(</tt><tt class="py-name">x2</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L296"></a><tt class="py-lineno">296</tt>  <tt class="py-line">        <tt class="py-name">q1</tt> <tt class="py-op">=</tt> <tt class="py-name">x1</tt> <tt class="py-op">*</tt> <tt class="py-op">(</tt><tt class="py-name">f</tt><tt class="py-op">(</tt><tt class="py-name">x2</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-name">f</tt><tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L297"></a><tt class="py-lineno">297</tt>  <tt class="py-line">        <tt class="py-name">q2</tt> <tt class="py-op">=</tt> <tt class="py-name">x2</tt> <tt class="py-op">*</tt> <tt class="py-op">(</tt><tt class="py-name">f</tt><tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-name">f</tt><tt class="py-op">(</tt><tt class="py-name">x1</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L298"></a><tt class="py-lineno">298</tt>  <tt class="py-line">        <tt class="py-name">xm</tt> <tt class="py-op">=</tt> <tt class="py-number">0.5</tt> <tt class="py-op">*</tt> <tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">*</tt><tt class="py-name">q0</tt> <tt class="py-op">+</tt> <tt class="py-name">x1</tt><tt class="py-op">*</tt><tt class="py-name">q1</tt> <tt class="py-op">+</tt> <tt class="py-name">x2</tt><tt class="py-op">*</tt><tt class="py-name">q2</tt><tt class="py-op">)</tt> <tt class="py-op">/</tt> <tt class="py-op">(</tt><tt class="py-name">q0</tt> <tt class="py-op">+</tt> <tt class="py-name">q1</tt> <tt class="py-op">+</tt> <tt class="py-name">q2</tt><tt class="py-op">)</tt> </tt>
<a name="L299"></a><tt class="py-lineno">299</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">xm</tt><tt class="py-op">,</tt> <tt class="py-name">e</tt> </tt>
</div></div><a name="L300"></a><tt class="py-lineno">300</tt>  <tt class="py-line"> </tt>
<a name="L301"></a><tt class="py-lineno">301</tt>  <tt class="py-line"> </tt>
<a name="L302"></a><tt class="py-lineno">302</tt>  <tt class="py-line"><tt class="py-comment">################################################################################</tt> </tt>
<a name="GoldenRule"></a><div id="GoldenRule-def"><a name="L303"></a><tt class="py-lineno">303</tt> <a class="py-toggle" href="#" id="GoldenRule-toggle" onclick="return toggle('GoldenRule');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="peach.optm.linear.GoldenRule-class.html">GoldenRule</a><tt class="py-op">(</tt><tt class="py-base-class">Optimizer</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="GoldenRule-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="GoldenRule-expanded"><a name="L304"></a><tt class="py-lineno">304</tt>  <tt class="py-line">    <tt class="py-docstring">'''</tt> </tt>
<a name="L305"></a><tt class="py-lineno">305</tt>  <tt class="py-line"><tt class="py-docstring">    Optimizer by the Golden Section Rule</tt> </tt>
<a name="L306"></a><tt class="py-lineno">306</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L307"></a><tt class="py-lineno">307</tt>  <tt class="py-line"><tt class="py-docstring">    This optimizer uses the golden rule to section an interval in search of the</tt> </tt>
<a name="L308"></a><tt class="py-lineno">308</tt>  <tt class="py-line"><tt class="py-docstring">    minimum. Using a simple heuristic, the interval is refined until an interval</tt> </tt>
<a name="L309"></a><tt class="py-lineno">309</tt>  <tt class="py-line"><tt class="py-docstring">    small enough to satisfy the error requirements is found.</tt> </tt>
<a name="L310"></a><tt class="py-lineno">310</tt>  <tt class="py-line"><tt class="py-docstring">    '''</tt> </tt>
<a name="GoldenRule.__init__"></a><div id="GoldenRule.__init__-def"><a name="L311"></a><tt class="py-lineno">311</tt> <a class="py-toggle" href="#" id="GoldenRule.__init__-toggle" onclick="return toggle('GoldenRule.__init__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="peach.optm.linear.GoldenRule-class.html#__init__">__init__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">f</tt><tt class="py-op">,</tt> <tt class="py-param">x0</tt><tt class="py-op">,</tt> <tt class="py-param">emax</tt><tt class="py-op">=</tt><tt class="py-number">1e-8</tt><tt class="py-op">,</tt> <tt class="py-param">imax</tt><tt class="py-op">=</tt><tt class="py-number">1000</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="GoldenRule.__init__-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="GoldenRule.__init__-expanded"><a name="L312"></a><tt class="py-lineno">312</tt>  <tt class="py-line">        <tt class="py-docstring">'''</tt> </tt>
<a name="L313"></a><tt class="py-lineno">313</tt>  <tt class="py-line"><tt class="py-docstring">        Initializes the optimizer.</tt> </tt>
<a name="L314"></a><tt class="py-lineno">314</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L315"></a><tt class="py-lineno">315</tt>  <tt class="py-line"><tt class="py-docstring">        To create an optimizer of this type, instantiate the class with the</tt> </tt>
<a name="L316"></a><tt class="py-lineno">316</tt>  <tt class="py-line"><tt class="py-docstring">        parameters given below:</tt> </tt>
<a name="L317"></a><tt class="py-lineno">317</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L318"></a><tt class="py-lineno">318</tt>  <tt class="py-line"><tt class="py-docstring">        :Parameters:</tt> </tt>
<a name="L319"></a><tt class="py-lineno">319</tt>  <tt class="py-line"><tt class="py-docstring">          f</tt> </tt>
<a name="L320"></a><tt class="py-lineno">320</tt>  <tt class="py-line"><tt class="py-docstring">            A one variable only function to be optimized. The function should</tt> </tt>
<a name="L321"></a><tt class="py-lineno">321</tt>  <tt class="py-line"><tt class="py-docstring">            have only one parameter and return the function value.</tt> </tt>
<a name="L322"></a><tt class="py-lineno">322</tt>  <tt class="py-line"><tt class="py-docstring">          x0</tt> </tt>
<a name="L323"></a><tt class="py-lineno">323</tt>  <tt class="py-line"><tt class="py-docstring">            First estimate of the minimum. The golden rule search needs two</tt> </tt>
<a name="L324"></a><tt class="py-lineno">324</tt>  <tt class="py-line"><tt class="py-docstring">            estimates to partition the interval. Thus, the first estimate must</tt> </tt>
<a name="L325"></a><tt class="py-lineno">325</tt>  <tt class="py-line"><tt class="py-docstring">            be a duple ``(xl, xh)``, with the property that ``xl &lt; xh``. Be</tt> </tt>
<a name="L326"></a><tt class="py-lineno">326</tt>  <tt class="py-line"><tt class="py-docstring">            aware, however, that no checking is done -- if the estimate doesn't</tt> </tt>
<a name="L327"></a><tt class="py-lineno">327</tt>  <tt class="py-line"><tt class="py-docstring">            correspond to this condition, in some point an exception will be</tt> </tt>
<a name="L328"></a><tt class="py-lineno">328</tt>  <tt class="py-line"><tt class="py-docstring">            raised.</tt> </tt>
<a name="L329"></a><tt class="py-lineno">329</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L330"></a><tt class="py-lineno">330</tt>  <tt class="py-line"><tt class="py-docstring">            Notice that, given the nature of the estimate of the golden rule</tt> </tt>
<a name="L331"></a><tt class="py-lineno">331</tt>  <tt class="py-line"><tt class="py-docstring">            method, it is not necessary to have a specific parameter to restrict</tt> </tt>
<a name="L332"></a><tt class="py-lineno">332</tt>  <tt class="py-line"><tt class="py-docstring">            the range of acceptable values -- it is already embedded in the</tt> </tt>
<a name="L333"></a><tt class="py-lineno">333</tt>  <tt class="py-line"><tt class="py-docstring">            estimate. If you need to restrict your estimate between an interval,</tt> </tt>
<a name="L334"></a><tt class="py-lineno">334</tt>  <tt class="py-line"><tt class="py-docstring">            just use its limits as ``xl`` and ``xh`` in the estimate.</tt> </tt>
<a name="L335"></a><tt class="py-lineno">335</tt>  <tt class="py-line"><tt class="py-docstring">          emax</tt> </tt>
<a name="L336"></a><tt class="py-lineno">336</tt>  <tt class="py-line"><tt class="py-docstring">            Maximum allowed error. The algorithm stops as soon as the error is</tt> </tt>
<a name="L337"></a><tt class="py-lineno">337</tt>  <tt class="py-line"><tt class="py-docstring">            below this level. The error is absolute.</tt> </tt>
<a name="L338"></a><tt class="py-lineno">338</tt>  <tt class="py-line"><tt class="py-docstring">          imax</tt> </tt>
<a name="L339"></a><tt class="py-lineno">339</tt>  <tt class="py-line"><tt class="py-docstring">            Maximum number of iterations, the algorithm stops as soon this</tt> </tt>
<a name="L340"></a><tt class="py-lineno">340</tt>  <tt class="py-line"><tt class="py-docstring">            number of iterations are executed, no matter what the error is at</tt> </tt>
<a name="L341"></a><tt class="py-lineno">341</tt>  <tt class="py-line"><tt class="py-docstring">            the moment.</tt> </tt>
<a name="L342"></a><tt class="py-lineno">342</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L343"></a><tt class="py-lineno">343</tt>  <tt class="py-line">        <tt id="link-42" class="py-name"><a title="peach.optm.base.Optimizer" class="py-name" href="#" onclick="return doclink('link-42', 'Optimizer', 'link-3');">Optimizer</a></tt><tt class="py-op">.</tt><tt id="link-43" class="py-name"><a title="peach.fuzzy.base.FuzzySet.__init__
peach.fuzzy.cmeans.FuzzyCMeans.__init__
peach.fuzzy.control.Controller.__init__
peach.fuzzy.control.Parametric.__init__
peach.fuzzy.mf.Bell.__init__
peach.fuzzy.mf.DecreasingRamp.__init__
peach.fuzzy.mf.DecreasingSigmoid.__init__
peach.fuzzy.mf.Gaussian.__init__
peach.fuzzy.mf.IncreasingRamp.__init__
peach.fuzzy.mf.IncreasingSigmoid.__init__
peach.fuzzy.mf.Membership.__init__
peach.fuzzy.mf.RaisedCosine.__init__
peach.fuzzy.mf.Smf.__init__
peach.fuzzy.mf.Trapezoid.__init__
peach.fuzzy.mf.Triangle.__init__
peach.fuzzy.mf.Zmf.__init__
peach.ga.base.GeneticAlgorithm.__init__
peach.ga.chromosome.Chromosome.__init__
peach.ga.crossover.OnePoint.__init__
peach.ga.crossover.TwoPoint.__init__
peach.ga.crossover.Uniform.__init__
peach.ga.fitness.Fitness.__init__
peach.ga.fitness.Ranking.__init__
peach.ga.mutation.BitToBit.__init__
peach.nn.af.Activation.__init__
peach.nn.af.ArcTan.__init__
peach.nn.af.Gaussian.__init__
peach.nn.af.Linear.__init__
peach.nn.af.Ramp.__init__
peach.nn.af.Sigmoid.__init__
peach.nn.af.Signum.__init__
peach.nn.af.TanH.__init__
peach.nn.af.Threshold.__init__
peach.nn.base.Layer.__init__
peach.nn.kmeans.KMeans.__init__
peach.nn.lrules.BackPropagation.__init__
peach.nn.lrules.Competitive.__init__
peach.nn.lrules.Cooperative.__init__
peach.nn.lrules.LMS.__init__
peach.nn.lrules.WinnerTakesAll.__init__
peach.nn.mem.Hopfield.__init__
peach.nn.nnet.FeedForward.__init__
peach.nn.nnet.GRNN.__init__
peach.nn.nnet.PNN.__init__
peach.nn.nnet.SOM.__init__
peach.nn.rbfn.RBFN.__init__
peach.optm.base.Optimizer.__init__
peach.optm.linear.Direct1D.__init__
peach.optm.linear.Fibonacci.__init__
peach.optm.linear.GoldenRule.__init__
peach.optm.linear.Interpolation.__init__
peach.optm.multivar.Direct.__init__
peach.optm.multivar.Gradient.__init__
peach.optm.multivar.MomentumGradient.__init__
peach.optm.multivar.Newton.__init__
peach.optm.quasinewton.BFGS.__init__
peach.optm.quasinewton.DFP.__init__
peach.optm.quasinewton.SR1.__init__
peach.optm.stochastic.CrossEntropy.__init__
peach.pso.acc.Accelerator.__init__
peach.pso.acc.StandardPSO.__init__
peach.pso.base.ParticleSwarmOptimizer.__init__
peach.sa.base.BinarySA.__init__
peach.sa.base.ContinuousSA.__init__
peach.sa.neighbor.BinaryNeighbor.__init__
peach.sa.neighbor.ContinuousNeighbor.__init__
peach.sa.neighbor.GaussianNeighbor.__init__
peach.sa.neighbor.InvertBitsNeighbor.__init__
peach.sa.neighbor.UniformNeighbor.__init__" class="py-name" href="#" onclick="return doclink('link-43', '__init__', 'link-5');">__init__</a></tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">)</tt> </tt>
<a name="L344"></a><tt class="py-lineno">344</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__f</tt> <tt class="py-op">=</tt> <tt class="py-name">f</tt> </tt>
<a name="L345"></a><tt class="py-lineno">345</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt> <tt class="py-op">=</tt> <tt class="py-name">x0</tt> </tt>
<a name="L346"></a><tt class="py-lineno">346</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__k</tt> <tt class="py-op">=</tt> <tt class="py-number">0.6180339887498949</tt>       <tt class="py-comment"># Golden ratio</tt> </tt>
<a name="L347"></a><tt class="py-lineno">347</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__emax</tt> <tt class="py-op">=</tt> <tt class="py-name">float</tt><tt class="py-op">(</tt><tt class="py-name">emax</tt><tt class="py-op">)</tt> </tt>
<a name="L348"></a><tt class="py-lineno">348</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__imax</tt> <tt class="py-op">=</tt> <tt class="py-name">int</tt><tt class="py-op">(</tt><tt class="py-name">imax</tt><tt class="py-op">)</tt> </tt>
</div><a name="L349"></a><tt class="py-lineno">349</tt>  <tt class="py-line"> </tt>
<a name="L350"></a><tt class="py-lineno">350</tt>  <tt class="py-line"> </tt>
<a name="GoldenRule.__get_x"></a><div id="GoldenRule.__get_x-def"><a name="L351"></a><tt class="py-lineno">351</tt> <a class="py-toggle" href="#" id="GoldenRule.__get_x-toggle" onclick="return toggle('GoldenRule.__get_x');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="peach.optm.linear.GoldenRule-class.html#__get_x">__get_x</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="GoldenRule.__get_x-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="GoldenRule.__get_x-expanded"><a name="L352"></a><tt class="py-lineno">352</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt> </tt>
</div><a name="L353"></a><tt class="py-lineno">353</tt>  <tt class="py-line"> </tt>
<a name="GoldenRule.__set_x"></a><div id="GoldenRule.__set_x-def"><a name="L354"></a><tt class="py-lineno">354</tt> <a class="py-toggle" href="#" id="GoldenRule.__set_x-toggle" onclick="return toggle('GoldenRule.__set_x');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="peach.optm.linear.GoldenRule-class.html#__set_x">__set_x</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x0</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="GoldenRule.__set_x-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="GoldenRule.__set_x-expanded"><a name="L355"></a><tt class="py-lineno">355</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-44" class="py-name"><a title="peach.ga.base.GeneticAlgorithm.restart
peach.optm.linear.Direct1D.restart
peach.optm.linear.Fibonacci.restart
peach.optm.linear.GoldenRule.restart
peach.optm.linear.Interpolation.restart
peach.optm.multivar.Direct.restart
peach.optm.multivar.Gradient.restart
peach.optm.multivar.MomentumGradient.restart
peach.optm.multivar.Newton.restart
peach.optm.quasinewton.BFGS.restart
peach.optm.quasinewton.DFP.restart
peach.optm.quasinewton.SR1.restart
peach.pso.base.ParticleSwarmOptimizer.restart
peach.sa.base.BinarySA.restart
peach.sa.base.ContinuousSA.restart" class="py-name" href="#" onclick="return doclink('link-44', 'restart', 'link-6');">restart</a></tt><tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">)</tt> </tt>
</div><a name="L356"></a><tt class="py-lineno">356</tt>  <tt class="py-line"> </tt>
<a name="L357"></a><tt class="py-lineno">357</tt>  <tt class="py-line">    <tt id="link-45" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-45', 'x', 'link-7');">x</a></tt> <tt class="py-op">=</tt> <tt class="py-name">property</tt><tt class="py-op">(</tt><tt id="link-46" class="py-name"><a title="peach.optm.linear.Direct1D.__get_x
peach.optm.linear.GoldenRule.__get_x
peach.optm.linear.Interpolation.__get_x
peach.optm.multivar.Direct.__get_x
peach.optm.multivar.Gradient.__get_x
peach.optm.multivar.MomentumGradient.__get_x
peach.optm.multivar.Newton.__get_x
peach.optm.quasinewton.DFP.__get_x
peach.optm.quasinewton.SR1.__get_x
peach.sa.base.BinarySA.__get_x
peach.sa.base.ContinuousSA.__get_x" class="py-name" href="#" onclick="return doclink('link-46', '__get_x', 'link-8');">__get_x</a></tt><tt class="py-op">,</tt> <tt id="link-47" class="py-name"><a title="peach.optm.linear.Direct1D.__set_x
peach.optm.linear.GoldenRule.__set_x
peach.optm.linear.Interpolation.__set_x
peach.optm.multivar.Direct.__set_x
peach.optm.multivar.Gradient.__set_x
peach.optm.multivar.MomentumGradient.__set_x
peach.optm.multivar.Newton.__set_x
peach.optm.quasinewton.DFP.__set_x
peach.optm.quasinewton.SR1.__set_x
peach.sa.base.BinarySA.__set_x
peach.sa.base.ContinuousSA.__set_x" class="py-name" href="#" onclick="return doclink('link-47', '__set_x', 'link-9');">__set_x</a></tt><tt class="py-op">)</tt> </tt>
<a name="L358"></a><tt class="py-lineno">358</tt>  <tt class="py-line">    <tt class="py-string">'''The estimate of the position of the minimum.'''</tt> </tt>
<a name="L359"></a><tt class="py-lineno">359</tt>  <tt class="py-line"> </tt>
<a name="L360"></a><tt class="py-lineno">360</tt>  <tt class="py-line"> </tt>
<a name="GoldenRule.restart"></a><div id="GoldenRule.restart-def"><a name="L361"></a><tt class="py-lineno">361</tt> <a class="py-toggle" href="#" id="GoldenRule.restart-toggle" onclick="return toggle('GoldenRule.restart');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="peach.optm.linear.GoldenRule-class.html#restart">restart</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x0</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="GoldenRule.restart-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="GoldenRule.restart-expanded"><a name="L362"></a><tt class="py-lineno">362</tt>  <tt class="py-line">        <tt class="py-docstring">'''</tt> </tt>
<a name="L363"></a><tt class="py-lineno">363</tt>  <tt class="py-line"><tt class="py-docstring">        Resets the optimizer, returning to its original state, and allowing to</tt> </tt>
<a name="L364"></a><tt class="py-lineno">364</tt>  <tt class="py-line"><tt class="py-docstring">        use a new first estimate.</tt> </tt>
<a name="L365"></a><tt class="py-lineno">365</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L366"></a><tt class="py-lineno">366</tt>  <tt class="py-line"><tt class="py-docstring">        :Parameters:</tt> </tt>
<a name="L367"></a><tt class="py-lineno">367</tt>  <tt class="py-line"><tt class="py-docstring">          x0</tt> </tt>
<a name="L368"></a><tt class="py-lineno">368</tt>  <tt class="py-line"><tt class="py-docstring">            The new value of the estimate of the minimum. The golden rule search</tt> </tt>
<a name="L369"></a><tt class="py-lineno">369</tt>  <tt class="py-line"><tt class="py-docstring">            needs two estimates to partition the interval. Thus, the estimate</tt> </tt>
<a name="L370"></a><tt class="py-lineno">370</tt>  <tt class="py-line"><tt class="py-docstring">            must be a duple ``(xl, xh)``, with the property that ``xl &lt; xh``.</tt> </tt>
<a name="L371"></a><tt class="py-lineno">371</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L372"></a><tt class="py-lineno">372</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt> <tt class="py-op">=</tt> <tt class="py-name">x0</tt> </tt>
</div><a name="L373"></a><tt class="py-lineno">373</tt>  <tt class="py-line"> </tt>
<a name="L374"></a><tt class="py-lineno">374</tt>  <tt class="py-line"> </tt>
<a name="GoldenRule.step"></a><div id="GoldenRule.step-def"><a name="L375"></a><tt class="py-lineno">375</tt> <a class="py-toggle" href="#" id="GoldenRule.step-toggle" onclick="return toggle('GoldenRule.step');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="peach.optm.linear.GoldenRule-class.html#step">step</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="GoldenRule.step-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="GoldenRule.step-expanded"><a name="L376"></a><tt class="py-lineno">376</tt>  <tt class="py-line">        <tt class="py-docstring">'''</tt> </tt>
<a name="L377"></a><tt class="py-lineno">377</tt>  <tt class="py-line"><tt class="py-docstring">        One step of the search.</tt> </tt>
<a name="L378"></a><tt class="py-lineno">378</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L379"></a><tt class="py-lineno">379</tt>  <tt class="py-line"><tt class="py-docstring">        In this method, the result of the step is dependent only of the given</tt> </tt>
<a name="L380"></a><tt class="py-lineno">380</tt>  <tt class="py-line"><tt class="py-docstring">        estimated, so it can be used for different kind of investigations on the</tt> </tt>
<a name="L381"></a><tt class="py-lineno">381</tt>  <tt class="py-line"><tt class="py-docstring">        same cost function.</tt> </tt>
<a name="L382"></a><tt class="py-lineno">382</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L383"></a><tt class="py-lineno">383</tt>  <tt class="py-line"><tt class="py-docstring">        :Returns:</tt> </tt>
<a name="L384"></a><tt class="py-lineno">384</tt>  <tt class="py-line"><tt class="py-docstring">          This method returns a tuple ``(x, e)``, where ``x`` is the updated</tt> </tt>
<a name="L385"></a><tt class="py-lineno">385</tt>  <tt class="py-line"><tt class="py-docstring">          duple of estimates of the minimum, and ``e`` is the estimated error.</tt> </tt>
<a name="L386"></a><tt class="py-lineno">386</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L387"></a><tt class="py-lineno">387</tt>  <tt class="py-line">        <tt class="py-name">x0</tt><tt class="py-op">,</tt> <tt class="py-name">x1</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt> </tt>
<a name="L388"></a><tt class="py-lineno">388</tt>  <tt class="py-line">        <tt class="py-name">f</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__f</tt> </tt>
<a name="L389"></a><tt class="py-lineno">389</tt>  <tt class="py-line">        <tt class="py-name">k</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__k</tt> </tt>
<a name="L390"></a><tt class="py-lineno">390</tt>  <tt class="py-line">        <tt class="py-name">k1</tt> <tt class="py-op">=</tt> <tt class="py-number">1</tt> <tt class="py-op">-</tt> <tt class="py-name">k</tt> </tt>
<a name="L391"></a><tt class="py-lineno">391</tt>  <tt class="py-line">        <tt class="py-name">xl</tt> <tt class="py-op">=</tt> <tt class="py-name">k</tt><tt class="py-op">*</tt><tt class="py-name">x0</tt> <tt class="py-op">+</tt> <tt class="py-name">k1</tt><tt class="py-op">*</tt><tt class="py-name">x1</tt> </tt>
<a name="L392"></a><tt class="py-lineno">392</tt>  <tt class="py-line">        <tt class="py-name">xh</tt> <tt class="py-op">=</tt> <tt class="py-name">k1</tt><tt class="py-op">*</tt><tt class="py-name">x0</tt> <tt class="py-op">+</tt> <tt class="py-name">k</tt><tt class="py-op">*</tt><tt class="py-name">x1</tt> </tt>
<a name="L393"></a><tt class="py-lineno">393</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">f</tt><tt class="py-op">(</tt><tt class="py-name">xl</tt><tt class="py-op">)</tt> <tt class="py-op">&gt;</tt> <tt class="py-name">f</tt><tt class="py-op">(</tt><tt class="py-name">xh</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L394"></a><tt class="py-lineno">394</tt>  <tt class="py-line">            <tt id="link-48" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-48', 'x', 'link-7');">x</a></tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">xl</tt><tt class="py-op">,</tt> <tt class="py-name">x1</tt><tt class="py-op">)</tt> </tt>
<a name="L395"></a><tt class="py-lineno">395</tt>  <tt class="py-line">            <tt class="py-name">e</tt> <tt class="py-op">=</tt> <tt id="link-49" class="py-name"><a title="peach.nn.rbfn.abs
peach.pso.base.abs" class="py-name" href="#" onclick="return doclink('link-49', 'abs', 'link-1');">abs</a></tt><tt class="py-op">(</tt><tt class="py-name">x1</tt> <tt class="py-op">-</tt> <tt class="py-name">xl</tt><tt class="py-op">)</tt> </tt>
<a name="L396"></a><tt class="py-lineno">396</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L397"></a><tt class="py-lineno">397</tt>  <tt class="py-line">            <tt id="link-50" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-50', 'x', 'link-7');">x</a></tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">,</tt> <tt class="py-name">xh</tt><tt class="py-op">)</tt> </tt>
<a name="L398"></a><tt class="py-lineno">398</tt>  <tt class="py-line">            <tt class="py-name">e</tt> <tt class="py-op">=</tt> <tt id="link-51" class="py-name"><a title="peach.nn.rbfn.abs
peach.pso.base.abs" class="py-name" href="#" onclick="return doclink('link-51', 'abs', 'link-1');">abs</a></tt><tt class="py-op">(</tt><tt class="py-name">xh</tt> <tt class="py-op">-</tt> <tt class="py-name">x0</tt><tt class="py-op">)</tt> </tt>
<a name="L399"></a><tt class="py-lineno">399</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt> <tt class="py-op">=</tt> <tt id="link-52" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-52', 'x', 'link-7');">x</a></tt> </tt>
<a name="L400"></a><tt class="py-lineno">400</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-53" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-53', 'x', 'link-7');">x</a></tt><tt class="py-op">,</tt> <tt class="py-name">e</tt> </tt>
</div><a name="L401"></a><tt class="py-lineno">401</tt>  <tt class="py-line"> </tt>
<a name="L402"></a><tt class="py-lineno">402</tt>  <tt class="py-line"> </tt>
<a name="GoldenRule.__call__"></a><div id="GoldenRule.__call__-def"><a name="L403"></a><tt class="py-lineno">403</tt> <a class="py-toggle" href="#" id="GoldenRule.__call__-toggle" onclick="return toggle('GoldenRule.__call__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="peach.optm.linear.GoldenRule-class.html#__call__">__call__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="GoldenRule.__call__-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="GoldenRule.__call__-expanded"><a name="L404"></a><tt class="py-lineno">404</tt>  <tt class="py-line">        <tt class="py-docstring">'''</tt> </tt>
<a name="L405"></a><tt class="py-lineno">405</tt>  <tt class="py-line"><tt class="py-docstring">        Transparently executes the search until the minimum is found. The stop</tt> </tt>
<a name="L406"></a><tt class="py-lineno">406</tt>  <tt class="py-line"><tt class="py-docstring">        criteria are the maximum error or the maximum number of iterations,</tt> </tt>
<a name="L407"></a><tt class="py-lineno">407</tt>  <tt class="py-line"><tt class="py-docstring">        whichever is reached first. Note that this is a ``__call__`` method, so</tt> </tt>
<a name="L408"></a><tt class="py-lineno">408</tt>  <tt class="py-line"><tt class="py-docstring">        the object is called as a function. This method returns a tuple</tt> </tt>
<a name="L409"></a><tt class="py-lineno">409</tt>  <tt class="py-line"><tt class="py-docstring">        ``(x, e)``, with the best estimate of the minimum and the error.</tt> </tt>
<a name="L410"></a><tt class="py-lineno">410</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L411"></a><tt class="py-lineno">411</tt>  <tt class="py-line"><tt class="py-docstring">        :Returns:</tt> </tt>
<a name="L412"></a><tt class="py-lineno">412</tt>  <tt class="py-line"><tt class="py-docstring">          This method returns a tuple ``(x, e)``, where ``x`` is the best</tt> </tt>
<a name="L413"></a><tt class="py-lineno">413</tt>  <tt class="py-line"><tt class="py-docstring">          estimate of the minimum, and ``e`` is the estimated error.</tt> </tt>
<a name="L414"></a><tt class="py-lineno">414</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L415"></a><tt class="py-lineno">415</tt>  <tt class="py-line">        <tt class="py-name">emax</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__emax</tt> </tt>
<a name="L416"></a><tt class="py-lineno">416</tt>  <tt class="py-line">        <tt class="py-name">imax</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__imax</tt> </tt>
<a name="L417"></a><tt class="py-lineno">417</tt>  <tt class="py-line">        <tt class="py-name">e</tt> <tt class="py-op">=</tt> <tt class="py-name">emax</tt> </tt>
<a name="L418"></a><tt class="py-lineno">418</tt>  <tt class="py-line">        <tt class="py-name">i</tt> <tt class="py-op">=</tt> <tt class="py-number">0</tt> </tt>
<a name="L419"></a><tt class="py-lineno">419</tt>  <tt class="py-line">        <tt class="py-keyword">while</tt> <tt class="py-name">e</tt> <tt class="py-op">&gt;</tt> <tt class="py-name">emax</tt><tt class="py-op">/</tt><tt class="py-number">2.</tt> <tt class="py-keyword">and</tt> <tt class="py-name">i</tt> <tt class="py-op">&lt;</tt> <tt class="py-name">imax</tt><tt class="py-op">:</tt> </tt>
<a name="L420"></a><tt class="py-lineno">420</tt>  <tt class="py-line">            <tt class="py-name">_</tt><tt class="py-op">,</tt> <tt class="py-name">e</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-54" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.step
peach.ga.base.GeneticAlgorithm.step
peach.nn.kmeans.KMeans.step
peach.nn.mem.Hopfield.step
peach.optm.base.Optimizer.step
peach.optm.linear.Direct1D.step
peach.optm.linear.Fibonacci.step
peach.optm.linear.GoldenRule.step
peach.optm.linear.Interpolation.step
peach.optm.multivar.Direct.step
peach.optm.multivar.Gradient.step
peach.optm.multivar.MomentumGradient.step
peach.optm.multivar.Newton.step
peach.optm.quasinewton.BFGS.step
peach.optm.quasinewton.DFP.step
peach.optm.quasinewton.SR1.step
peach.optm.stochastic.CrossEntropy.step
peach.pso.base.ParticleSwarmOptimizer.step
peach.sa.base.BinarySA.step
peach.sa.base.ContinuousSA.step" class="py-name" href="#" onclick="return doclink('link-54', 'step', 'link-23');">step</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L421"></a><tt class="py-lineno">421</tt>  <tt class="py-line">            <tt class="py-name">i</tt> <tt class="py-op">=</tt> <tt class="py-name">i</tt> <tt class="py-op">+</tt> <tt class="py-number">1</tt> </tt>
<a name="L422"></a><tt class="py-lineno">422</tt>  <tt class="py-line">        <tt class="py-name">xl</tt><tt class="py-op">,</tt> <tt class="py-name">xh</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt> </tt>
<a name="L423"></a><tt class="py-lineno">423</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-number">0.5</tt> <tt class="py-op">*</tt> <tt class="py-op">(</tt><tt class="py-name">xl</tt> <tt class="py-op">+</tt> <tt class="py-name">xh</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">e</tt> </tt>
</div></div><a name="L424"></a><tt class="py-lineno">424</tt>  <tt class="py-line"> </tt>
<a name="L425"></a><tt class="py-lineno">425</tt>  <tt class="py-line"> </tt>
<a name="L426"></a><tt class="py-lineno">426</tt>  <tt class="py-line"><tt class="py-comment">################################################################################</tt> </tt>
<a name="Fibonacci"></a><div id="Fibonacci-def"><a name="L427"></a><tt class="py-lineno">427</tt> <a class="py-toggle" href="#" id="Fibonacci-toggle" onclick="return toggle('Fibonacci');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="peach.optm.linear.Fibonacci-class.html">Fibonacci</a><tt class="py-op">(</tt><tt class="py-base-class">Optimizer</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Fibonacci-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="Fibonacci-expanded"><a name="L428"></a><tt class="py-lineno">428</tt>  <tt class="py-line">    <tt class="py-docstring">'''</tt> </tt>
<a name="L429"></a><tt class="py-lineno">429</tt>  <tt class="py-line"><tt class="py-docstring">    Optimization by the Golden Rule Section, estimated by Fibonacci numbers.</tt> </tt>
<a name="L430"></a><tt class="py-lineno">430</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L431"></a><tt class="py-lineno">431</tt>  <tt class="py-line"><tt class="py-docstring">    This optimizer uses the golden rule to section an interval in search of the</tt> </tt>
<a name="L432"></a><tt class="py-lineno">432</tt>  <tt class="py-line"><tt class="py-docstring">    minimum. Using a simple heuristic, the interval is refined until an interval</tt> </tt>
<a name="L433"></a><tt class="py-lineno">433</tt>  <tt class="py-line"><tt class="py-docstring">    small enough to satisfy the error requirements is found. The golden section</tt> </tt>
<a name="L434"></a><tt class="py-lineno">434</tt>  <tt class="py-line"><tt class="py-docstring">    is estimated at each step using Fibonacci numbers. This can be useful in</tt> </tt>
<a name="L435"></a><tt class="py-lineno">435</tt>  <tt class="py-line"><tt class="py-docstring">    situations where only integer numbers should be used.</tt> </tt>
<a name="L436"></a><tt class="py-lineno">436</tt>  <tt class="py-line"><tt class="py-docstring">    '''</tt> </tt>
<a name="Fibonacci.__init__"></a><div id="Fibonacci.__init__-def"><a name="L437"></a><tt class="py-lineno">437</tt> <a class="py-toggle" href="#" id="Fibonacci.__init__-toggle" onclick="return toggle('Fibonacci.__init__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="peach.optm.linear.Fibonacci-class.html#__init__">__init__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">f</tt><tt class="py-op">,</tt> <tt class="py-param">x0</tt><tt class="py-op">,</tt> <tt class="py-param">emax</tt><tt class="py-op">=</tt><tt class="py-number">1e-8</tt><tt class="py-op">,</tt> <tt class="py-param">imax</tt><tt class="py-op">=</tt><tt class="py-number">1000</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Fibonacci.__init__-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Fibonacci.__init__-expanded"><a name="L438"></a><tt class="py-lineno">438</tt>  <tt class="py-line">        <tt class="py-docstring">'''</tt> </tt>
<a name="L439"></a><tt class="py-lineno">439</tt>  <tt class="py-line"><tt class="py-docstring">        Initializes the optimizer.</tt> </tt>
<a name="L440"></a><tt class="py-lineno">440</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L441"></a><tt class="py-lineno">441</tt>  <tt class="py-line"><tt class="py-docstring">        To create an optimizer of this type, instantiate the class with the</tt> </tt>
<a name="L442"></a><tt class="py-lineno">442</tt>  <tt class="py-line"><tt class="py-docstring">        parameters given below:</tt> </tt>
<a name="L443"></a><tt class="py-lineno">443</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L444"></a><tt class="py-lineno">444</tt>  <tt class="py-line"><tt class="py-docstring">        :Parameters:</tt> </tt>
<a name="L445"></a><tt class="py-lineno">445</tt>  <tt class="py-line"><tt class="py-docstring">          f</tt> </tt>
<a name="L446"></a><tt class="py-lineno">446</tt>  <tt class="py-line"><tt class="py-docstring">            A one variable only function to be optimized. The function should</tt> </tt>
<a name="L447"></a><tt class="py-lineno">447</tt>  <tt class="py-line"><tt class="py-docstring">            have only one parameter and return the function value.</tt> </tt>
<a name="L448"></a><tt class="py-lineno">448</tt>  <tt class="py-line"><tt class="py-docstring">          x0</tt> </tt>
<a name="L449"></a><tt class="py-lineno">449</tt>  <tt class="py-line"><tt class="py-docstring">            First estimate of the minimum. The Fibonacci search needs two</tt> </tt>
<a name="L450"></a><tt class="py-lineno">450</tt>  <tt class="py-line"><tt class="py-docstring">            estimates to partition the interval. Thus, the first estimate must</tt> </tt>
<a name="L451"></a><tt class="py-lineno">451</tt>  <tt class="py-line"><tt class="py-docstring">            be a duple ``(xl, xh)``, with the property that ``xl &lt; xh``. Be</tt> </tt>
<a name="L452"></a><tt class="py-lineno">452</tt>  <tt class="py-line"><tt class="py-docstring">            aware, however, that no checking is done -- if the estimate doesn't</tt> </tt>
<a name="L453"></a><tt class="py-lineno">453</tt>  <tt class="py-line"><tt class="py-docstring">            correspond to this condition, in some point an exception will be</tt> </tt>
<a name="L454"></a><tt class="py-lineno">454</tt>  <tt class="py-line"><tt class="py-docstring">            raised.</tt> </tt>
<a name="L455"></a><tt class="py-lineno">455</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L456"></a><tt class="py-lineno">456</tt>  <tt class="py-line"><tt class="py-docstring">            Notice that, given the nature of the estimate of the Fibonacci</tt> </tt>
<a name="L457"></a><tt class="py-lineno">457</tt>  <tt class="py-line"><tt class="py-docstring">            method, it is not necessary to have a specific parameter to restrict</tt> </tt>
<a name="L458"></a><tt class="py-lineno">458</tt>  <tt class="py-line"><tt class="py-docstring">            the range of acceptable values -- it is already embedded in the</tt> </tt>
<a name="L459"></a><tt class="py-lineno">459</tt>  <tt class="py-line"><tt class="py-docstring">            estimate. If you need to restrict your estimate between an interval,</tt> </tt>
<a name="L460"></a><tt class="py-lineno">460</tt>  <tt class="py-line"><tt class="py-docstring">            just use its limits as ``xl`` and ``xh`` in the estimate.</tt> </tt>
<a name="L461"></a><tt class="py-lineno">461</tt>  <tt class="py-line"><tt class="py-docstring">          emax</tt> </tt>
<a name="L462"></a><tt class="py-lineno">462</tt>  <tt class="py-line"><tt class="py-docstring">            Maximum allowed error. The algorithm stops as soon as the error is</tt> </tt>
<a name="L463"></a><tt class="py-lineno">463</tt>  <tt class="py-line"><tt class="py-docstring">            below this level. The error is absolute.</tt> </tt>
<a name="L464"></a><tt class="py-lineno">464</tt>  <tt class="py-line"><tt class="py-docstring">          imax</tt> </tt>
<a name="L465"></a><tt class="py-lineno">465</tt>  <tt class="py-line"><tt class="py-docstring">            Maximum number of iterations, the algorithm stops as soon this</tt> </tt>
<a name="L466"></a><tt class="py-lineno">466</tt>  <tt class="py-line"><tt class="py-docstring">            number of iterations are executed, no matter what the error is at</tt> </tt>
<a name="L467"></a><tt class="py-lineno">467</tt>  <tt class="py-line"><tt class="py-docstring">            the moment.</tt> </tt>
<a name="L468"></a><tt class="py-lineno">468</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L469"></a><tt class="py-lineno">469</tt>  <tt class="py-line">        <tt id="link-55" class="py-name"><a title="peach.optm.base.Optimizer" class="py-name" href="#" onclick="return doclink('link-55', 'Optimizer', 'link-3');">Optimizer</a></tt><tt class="py-op">.</tt><tt id="link-56" class="py-name"><a title="peach.fuzzy.base.FuzzySet.__init__
peach.fuzzy.cmeans.FuzzyCMeans.__init__
peach.fuzzy.control.Controller.__init__
peach.fuzzy.control.Parametric.__init__
peach.fuzzy.mf.Bell.__init__
peach.fuzzy.mf.DecreasingRamp.__init__
peach.fuzzy.mf.DecreasingSigmoid.__init__
peach.fuzzy.mf.Gaussian.__init__
peach.fuzzy.mf.IncreasingRamp.__init__
peach.fuzzy.mf.IncreasingSigmoid.__init__
peach.fuzzy.mf.Membership.__init__
peach.fuzzy.mf.RaisedCosine.__init__
peach.fuzzy.mf.Smf.__init__
peach.fuzzy.mf.Trapezoid.__init__
peach.fuzzy.mf.Triangle.__init__
peach.fuzzy.mf.Zmf.__init__
peach.ga.base.GeneticAlgorithm.__init__
peach.ga.chromosome.Chromosome.__init__
peach.ga.crossover.OnePoint.__init__
peach.ga.crossover.TwoPoint.__init__
peach.ga.crossover.Uniform.__init__
peach.ga.fitness.Fitness.__init__
peach.ga.fitness.Ranking.__init__
peach.ga.mutation.BitToBit.__init__
peach.nn.af.Activation.__init__
peach.nn.af.ArcTan.__init__
peach.nn.af.Gaussian.__init__
peach.nn.af.Linear.__init__
peach.nn.af.Ramp.__init__
peach.nn.af.Sigmoid.__init__
peach.nn.af.Signum.__init__
peach.nn.af.TanH.__init__
peach.nn.af.Threshold.__init__
peach.nn.base.Layer.__init__
peach.nn.kmeans.KMeans.__init__
peach.nn.lrules.BackPropagation.__init__
peach.nn.lrules.Competitive.__init__
peach.nn.lrules.Cooperative.__init__
peach.nn.lrules.LMS.__init__
peach.nn.lrules.WinnerTakesAll.__init__
peach.nn.mem.Hopfield.__init__
peach.nn.nnet.FeedForward.__init__
peach.nn.nnet.GRNN.__init__
peach.nn.nnet.PNN.__init__
peach.nn.nnet.SOM.__init__
peach.nn.rbfn.RBFN.__init__
peach.optm.base.Optimizer.__init__
peach.optm.linear.Direct1D.__init__
peach.optm.linear.Fibonacci.__init__
peach.optm.linear.GoldenRule.__init__
peach.optm.linear.Interpolation.__init__
peach.optm.multivar.Direct.__init__
peach.optm.multivar.Gradient.__init__
peach.optm.multivar.MomentumGradient.__init__
peach.optm.multivar.Newton.__init__
peach.optm.quasinewton.BFGS.__init__
peach.optm.quasinewton.DFP.__init__
peach.optm.quasinewton.SR1.__init__
peach.optm.stochastic.CrossEntropy.__init__
peach.pso.acc.Accelerator.__init__
peach.pso.acc.StandardPSO.__init__
peach.pso.base.ParticleSwarmOptimizer.__init__
peach.sa.base.BinarySA.__init__
peach.sa.base.ContinuousSA.__init__
peach.sa.neighbor.BinaryNeighbor.__init__
peach.sa.neighbor.ContinuousNeighbor.__init__
peach.sa.neighbor.GaussianNeighbor.__init__
peach.sa.neighbor.InvertBitsNeighbor.__init__
peach.sa.neighbor.UniformNeighbor.__init__" class="py-name" href="#" onclick="return doclink('link-56', '__init__', 'link-5');">__init__</a></tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">)</tt> </tt>
<a name="L470"></a><tt class="py-lineno">470</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__f</tt> <tt class="py-op">=</tt> <tt class="py-name">f</tt> </tt>
<a name="L471"></a><tt class="py-lineno">471</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt> <tt class="py-op">=</tt> <tt class="py-name">x0</tt> </tt>
<a name="L472"></a><tt class="py-lineno">472</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__k1</tt> <tt class="py-op">=</tt> <tt class="py-number">1.</tt> </tt>
<a name="L473"></a><tt class="py-lineno">473</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__k2</tt> <tt class="py-op">=</tt> <tt class="py-number">1.</tt> </tt>
<a name="L474"></a><tt class="py-lineno">474</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__emax</tt> <tt class="py-op">=</tt> <tt class="py-name">float</tt><tt class="py-op">(</tt><tt class="py-name">emax</tt><tt class="py-op">)</tt> </tt>
<a name="L475"></a><tt class="py-lineno">475</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__imax</tt> <tt class="py-op">=</tt> <tt class="py-name">int</tt><tt class="py-op">(</tt><tt class="py-name">imax</tt><tt class="py-op">)</tt> </tt>
</div><a name="L476"></a><tt class="py-lineno">476</tt>  <tt class="py-line"> </tt>
<a name="L477"></a><tt class="py-lineno">477</tt>  <tt class="py-line"> </tt>
<a name="Fibonacci.restart"></a><div id="Fibonacci.restart-def"><a name="L478"></a><tt class="py-lineno">478</tt> <a class="py-toggle" href="#" id="Fibonacci.restart-toggle" onclick="return toggle('Fibonacci.restart');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="peach.optm.linear.Fibonacci-class.html#restart">restart</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x0</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Fibonacci.restart-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Fibonacci.restart-expanded"><a name="L479"></a><tt class="py-lineno">479</tt>  <tt class="py-line">        <tt class="py-docstring">'''</tt> </tt>
<a name="L480"></a><tt class="py-lineno">480</tt>  <tt class="py-line"><tt class="py-docstring">        Resets the optimizer, returning to its original state, and allowing to</tt> </tt>
<a name="L481"></a><tt class="py-lineno">481</tt>  <tt class="py-line"><tt class="py-docstring">        use a new first estimate.</tt> </tt>
<a name="L482"></a><tt class="py-lineno">482</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L483"></a><tt class="py-lineno">483</tt>  <tt class="py-line"><tt class="py-docstring">        :Parameters:</tt> </tt>
<a name="L484"></a><tt class="py-lineno">484</tt>  <tt class="py-line"><tt class="py-docstring">          x0</tt> </tt>
<a name="L485"></a><tt class="py-lineno">485</tt>  <tt class="py-line"><tt class="py-docstring">            The new value of the estimate of the minimum. The Fibonacci search</tt> </tt>
<a name="L486"></a><tt class="py-lineno">486</tt>  <tt class="py-line"><tt class="py-docstring">            needs two estimates to partition the interval. Thus, the estimate</tt> </tt>
<a name="L487"></a><tt class="py-lineno">487</tt>  <tt class="py-line"><tt class="py-docstring">            must be a duple ``(xl, xh)``, with the property that ``xl &lt; xh``. Be</tt> </tt>
<a name="L488"></a><tt class="py-lineno">488</tt>  <tt class="py-line"><tt class="py-docstring">            aware, however, that no checking is done -- if the estimate doesn't</tt> </tt>
<a name="L489"></a><tt class="py-lineno">489</tt>  <tt class="py-line"><tt class="py-docstring">            correspond to this condition, in some point an exception will be</tt> </tt>
<a name="L490"></a><tt class="py-lineno">490</tt>  <tt class="py-line"><tt class="py-docstring">            raised.</tt> </tt>
<a name="L491"></a><tt class="py-lineno">491</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L492"></a><tt class="py-lineno">492</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt> <tt class="py-op">=</tt> <tt class="py-name">x0</tt> </tt>
</div><a name="L493"></a><tt class="py-lineno">493</tt>  <tt class="py-line"> </tt>
<a name="L494"></a><tt class="py-lineno">494</tt>  <tt class="py-line"> </tt>
<a name="Fibonacci.step"></a><div id="Fibonacci.step-def"><a name="L495"></a><tt class="py-lineno">495</tt> <a class="py-toggle" href="#" id="Fibonacci.step-toggle" onclick="return toggle('Fibonacci.step');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="peach.optm.linear.Fibonacci-class.html#step">step</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Fibonacci.step-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Fibonacci.step-expanded"><a name="L496"></a><tt class="py-lineno">496</tt>  <tt class="py-line">        <tt class="py-docstring">'''</tt> </tt>
<a name="L497"></a><tt class="py-lineno">497</tt>  <tt class="py-line"><tt class="py-docstring">        One step of the search.</tt> </tt>
<a name="L498"></a><tt class="py-lineno">498</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L499"></a><tt class="py-lineno">499</tt>  <tt class="py-line"><tt class="py-docstring">        In this method, the result of the step is highly dependent of the steps</tt> </tt>
<a name="L500"></a><tt class="py-lineno">500</tt>  <tt class="py-line"><tt class="py-docstring">        executed before, as the estimate of the golden ratio is updated at each</tt> </tt>
<a name="L501"></a><tt class="py-lineno">501</tt>  <tt class="py-line"><tt class="py-docstring">        call to this method.</tt> </tt>
<a name="L502"></a><tt class="py-lineno">502</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L503"></a><tt class="py-lineno">503</tt>  <tt class="py-line"><tt class="py-docstring">        :Returns:</tt> </tt>
<a name="L504"></a><tt class="py-lineno">504</tt>  <tt class="py-line"><tt class="py-docstring">          This method returns a tuple ``(x, e)``, where ``x`` is the updated</tt> </tt>
<a name="L505"></a><tt class="py-lineno">505</tt>  <tt class="py-line"><tt class="py-docstring">          duple of estimates of the minimum, and ``e`` is the estimated error.</tt> </tt>
<a name="L506"></a><tt class="py-lineno">506</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L507"></a><tt class="py-lineno">507</tt>  <tt class="py-line">        <tt class="py-name">x0</tt><tt class="py-op">,</tt> <tt class="py-name">x1</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt> </tt>
<a name="L508"></a><tt class="py-lineno">508</tt>  <tt class="py-line">        <tt class="py-name">f</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__f</tt> </tt>
<a name="L509"></a><tt class="py-lineno">509</tt>  <tt class="py-line">        <tt class="py-name">k1</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__k1</tt> </tt>
<a name="L510"></a><tt class="py-lineno">510</tt>  <tt class="py-line">        <tt class="py-name">k2</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__k2</tt> </tt>
<a name="L511"></a><tt class="py-lineno">511</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__k1</tt> <tt class="py-op">=</tt> <tt class="py-name">k2</tt> </tt>
<a name="L512"></a><tt class="py-lineno">512</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__k2</tt> <tt class="py-op">=</tt> <tt class="py-name">k1</tt> <tt class="py-op">+</tt> <tt class="py-name">k2</tt> </tt>
<a name="L513"></a><tt class="py-lineno">513</tt>  <tt class="py-line">        <tt class="py-name">k</tt> <tt class="py-op">=</tt> <tt class="py-name">k1</tt> <tt class="py-op">/</tt> <tt class="py-name">k2</tt> </tt>
<a name="L514"></a><tt class="py-lineno">514</tt>  <tt class="py-line">        <tt class="py-name">k1</tt> <tt class="py-op">=</tt> <tt class="py-number">1</tt> <tt class="py-op">-</tt> <tt class="py-name">k</tt> </tt>
<a name="L515"></a><tt class="py-lineno">515</tt>  <tt class="py-line">        <tt class="py-name">xl</tt> <tt class="py-op">=</tt> <tt class="py-name">k</tt><tt class="py-op">*</tt><tt class="py-name">x0</tt> <tt class="py-op">+</tt> <tt class="py-name">k1</tt><tt class="py-op">*</tt><tt class="py-name">x1</tt> </tt>
<a name="L516"></a><tt class="py-lineno">516</tt>  <tt class="py-line">        <tt class="py-name">xh</tt> <tt class="py-op">=</tt> <tt class="py-name">k1</tt><tt class="py-op">*</tt><tt class="py-name">x0</tt> <tt class="py-op">+</tt> <tt class="py-name">k</tt><tt class="py-op">*</tt><tt class="py-name">x1</tt> </tt>
<a name="L517"></a><tt class="py-lineno">517</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">f</tt><tt class="py-op">(</tt><tt class="py-name">xl</tt><tt class="py-op">)</tt> <tt class="py-op">&gt;</tt> <tt class="py-name">f</tt><tt class="py-op">(</tt><tt class="py-name">xh</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L518"></a><tt class="py-lineno">518</tt>  <tt class="py-line">            <tt id="link-57" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-57', 'x', 'link-7');">x</a></tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">xl</tt><tt class="py-op">,</tt> <tt class="py-name">x1</tt><tt class="py-op">)</tt> </tt>
<a name="L519"></a><tt class="py-lineno">519</tt>  <tt class="py-line">            <tt class="py-name">e</tt> <tt class="py-op">=</tt> <tt id="link-58" class="py-name"><a title="peach.nn.rbfn.abs
peach.pso.base.abs" class="py-name" href="#" onclick="return doclink('link-58', 'abs', 'link-1');">abs</a></tt><tt class="py-op">(</tt><tt class="py-name">x1</tt> <tt class="py-op">-</tt> <tt class="py-name">xl</tt><tt class="py-op">)</tt> </tt>
<a name="L520"></a><tt class="py-lineno">520</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L521"></a><tt class="py-lineno">521</tt>  <tt class="py-line">            <tt id="link-59" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-59', 'x', 'link-7');">x</a></tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">,</tt> <tt class="py-name">xh</tt><tt class="py-op">)</tt> </tt>
<a name="L522"></a><tt class="py-lineno">522</tt>  <tt class="py-line">            <tt class="py-name">e</tt> <tt class="py-op">=</tt> <tt id="link-60" class="py-name"><a title="peach.nn.rbfn.abs
peach.pso.base.abs" class="py-name" href="#" onclick="return doclink('link-60', 'abs', 'link-1');">abs</a></tt><tt class="py-op">(</tt><tt class="py-name">xh</tt> <tt class="py-op">-</tt> <tt class="py-name">x0</tt><tt class="py-op">)</tt> </tt>
<a name="L523"></a><tt class="py-lineno">523</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt> <tt class="py-op">=</tt> <tt id="link-61" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-61', 'x', 'link-7');">x</a></tt> </tt>
<a name="L524"></a><tt class="py-lineno">524</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-62" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-62', 'x', 'link-7');">x</a></tt><tt class="py-op">,</tt> <tt class="py-name">e</tt> </tt>
</div><a name="L525"></a><tt class="py-lineno">525</tt>  <tt class="py-line"> </tt>
<a name="L526"></a><tt class="py-lineno">526</tt>  <tt class="py-line"> </tt>
<a name="Fibonacci.__call__"></a><div id="Fibonacci.__call__-def"><a name="L527"></a><tt class="py-lineno">527</tt> <a class="py-toggle" href="#" id="Fibonacci.__call__-toggle" onclick="return toggle('Fibonacci.__call__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="peach.optm.linear.Fibonacci-class.html#__call__">__call__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Fibonacci.__call__-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Fibonacci.__call__-expanded"><a name="L528"></a><tt class="py-lineno">528</tt>  <tt class="py-line">        <tt class="py-docstring">'''</tt> </tt>
<a name="L529"></a><tt class="py-lineno">529</tt>  <tt class="py-line"><tt class="py-docstring">        Transparently executes the search until the minimum is found. The stop</tt> </tt>
<a name="L530"></a><tt class="py-lineno">530</tt>  <tt class="py-line"><tt class="py-docstring">        criteria are the maximum error or the maximum number of iterations,</tt> </tt>
<a name="L531"></a><tt class="py-lineno">531</tt>  <tt class="py-line"><tt class="py-docstring">        whichever is reached first. Note that this is a ``__call__`` method, so</tt> </tt>
<a name="L532"></a><tt class="py-lineno">532</tt>  <tt class="py-line"><tt class="py-docstring">        the object is called as a function. This method returns a tuple</tt> </tt>
<a name="L533"></a><tt class="py-lineno">533</tt>  <tt class="py-line"><tt class="py-docstring">        ``(x, e)``, with the best estimate of the minimum and the error.</tt> </tt>
<a name="L534"></a><tt class="py-lineno">534</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L535"></a><tt class="py-lineno">535</tt>  <tt class="py-line"><tt class="py-docstring">        :Returns:</tt> </tt>
<a name="L536"></a><tt class="py-lineno">536</tt>  <tt class="py-line"><tt class="py-docstring">          This method returns a tuple ``(x, e)``, where ``x`` is the best</tt> </tt>
<a name="L537"></a><tt class="py-lineno">537</tt>  <tt class="py-line"><tt class="py-docstring">          estimate of the minimum, and ``e`` is the estimated error.</tt> </tt>
<a name="L538"></a><tt class="py-lineno">538</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L539"></a><tt class="py-lineno">539</tt>  <tt class="py-line">        <tt class="py-name">emax</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__emax</tt> </tt>
<a name="L540"></a><tt class="py-lineno">540</tt>  <tt class="py-line">        <tt class="py-name">imax</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__imax</tt> </tt>
<a name="L541"></a><tt class="py-lineno">541</tt>  <tt class="py-line">        <tt class="py-name">e</tt> <tt class="py-op">=</tt> <tt class="py-name">emax</tt> </tt>
<a name="L542"></a><tt class="py-lineno">542</tt>  <tt class="py-line">        <tt class="py-name">i</tt> <tt class="py-op">=</tt> <tt class="py-number">0</tt> </tt>
<a name="L543"></a><tt class="py-lineno">543</tt>  <tt class="py-line">        <tt class="py-keyword">while</tt> <tt class="py-name">e</tt> <tt class="py-op">&gt;</tt> <tt class="py-name">emax</tt><tt class="py-op">/</tt><tt class="py-number">2.</tt> <tt class="py-keyword">and</tt> <tt class="py-name">i</tt> <tt class="py-op">&lt;</tt> <tt class="py-name">imax</tt><tt class="py-op">:</tt> </tt>
<a name="L544"></a><tt class="py-lineno">544</tt>  <tt class="py-line">            <tt class="py-name">_</tt><tt class="py-op">,</tt> <tt class="py-name">e</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-63" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.step
peach.ga.base.GeneticAlgorithm.step
peach.nn.kmeans.KMeans.step
peach.nn.mem.Hopfield.step
peach.optm.base.Optimizer.step
peach.optm.linear.Direct1D.step
peach.optm.linear.Fibonacci.step
peach.optm.linear.GoldenRule.step
peach.optm.linear.Interpolation.step
peach.optm.multivar.Direct.step
peach.optm.multivar.Gradient.step
peach.optm.multivar.MomentumGradient.step
peach.optm.multivar.Newton.step
peach.optm.quasinewton.BFGS.step
peach.optm.quasinewton.DFP.step
peach.optm.quasinewton.SR1.step
peach.optm.stochastic.CrossEntropy.step
peach.pso.base.ParticleSwarmOptimizer.step
peach.sa.base.BinarySA.step
peach.sa.base.ContinuousSA.step" class="py-name" href="#" onclick="return doclink('link-63', 'step', 'link-23');">step</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L545"></a><tt class="py-lineno">545</tt>  <tt class="py-line">            <tt class="py-name">i</tt> <tt class="py-op">=</tt> <tt class="py-name">i</tt> <tt class="py-op">+</tt> <tt class="py-number">1</tt> </tt>
<a name="L546"></a><tt class="py-lineno">546</tt>  <tt class="py-line">        <tt class="py-name">xl</tt><tt class="py-op">,</tt> <tt class="py-name">xh</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">__x</tt> </tt>
<a name="L547"></a><tt class="py-lineno">547</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-number">0.5</tt><tt class="py-op">*</tt> <tt class="py-op">(</tt><tt class="py-name">xl</tt> <tt class="py-op">+</tt> <tt class="py-name">xh</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">e</tt> </tt>
</div></div><a name="L548"></a><tt class="py-lineno">548</tt>  <tt class="py-line"> </tt>
<a name="L549"></a><tt class="py-lineno">549</tt>  <tt class="py-line"> </tt>
<a name="L550"></a><tt class="py-lineno">550</tt>  <tt class="py-line"><tt class="py-comment">################################################################################</tt> </tt>
<a name="L551"></a><tt class="py-lineno">551</tt>  <tt class="py-line"><tt class="py-comment"># Test</tt> </tt>
<a name="L552"></a><tt class="py-lineno">552</tt>  <tt class="py-line"><tt class="py-keyword">if</tt> <tt class="py-name">__name__</tt> <tt class="py-op">==</tt> <tt class="py-string">"__main__"</tt><tt class="py-op">:</tt> </tt>
<a name="L553"></a><tt class="py-lineno">553</tt>  <tt class="py-line"> </tt>
<a name="L554"></a><tt class="py-lineno">554</tt>  <tt class="py-line">    <tt class="py-comment"># Rosenbrock function</tt> </tt>
<a name="f"></a><div id="f-def"><a name="L555"></a><tt class="py-lineno">555</tt> <a class="py-toggle" href="#" id="f-toggle" onclick="return toggle('f');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="peach.optm.linear-module.html#f">f</a><tt class="py-op">(</tt><tt class="py-param">x</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="f-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="f-expanded"><a name="L556"></a><tt class="py-lineno">556</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-op">(</tt><tt class="py-number">1.</tt><tt class="py-op">-</tt><tt id="link-64" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-64', 'x', 'link-7');">x</a></tt><tt class="py-op">)</tt><tt class="py-op">**</tt><tt class="py-number">2.</tt> <tt class="py-op">+</tt> <tt class="py-op">(</tt><tt class="py-number">1.</tt><tt class="py-op">-</tt><tt id="link-65" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-65', 'x', 'link-7');">x</a></tt><tt class="py-op">*</tt><tt id="link-66" class="py-name"><a title="peach.fuzzy.cmeans.FuzzyCMeans.x
peach.optm.linear.Direct1D.x
peach.optm.linear.GoldenRule.x
peach.optm.linear.Interpolation.x
peach.optm.multivar.Direct.x
peach.optm.multivar.Gradient.x
peach.optm.multivar.MomentumGradient.x
peach.optm.multivar.Newton.x
peach.optm.quasinewton.DFP.x
peach.optm.quasinewton.SR1.x
peach.sa.base.BinarySA.x
peach.sa.base.ContinuousSA.x" class="py-name" href="#" onclick="return doclink('link-66', 'x', 'link-7');">x</a></tt><tt class="py-op">)</tt><tt class="py-op">**</tt><tt class="py-number">2.</tt> </tt>
</div><a name="L557"></a><tt class="py-lineno">557</tt>  <tt class="py-line"> </tt>
<a name="L558"></a><tt class="py-lineno">558</tt>  <tt class="py-line">    <tt id="link-67" class="py-name" targets="Module peach.optm.linear=peach.optm.linear-module.html"><a title="peach.optm.linear" class="py-name" href="#" onclick="return doclink('link-67', 'linear', 'link-67');">linear</a></tt> <tt class="py-op">=</tt> <tt id="link-68" class="py-name" targets="Class peach.optm.linear.Direct1D=peach.optm.linear.Direct1D-class.html"><a title="peach.optm.linear.Direct1D" class="py-name" href="#" onclick="return doclink('link-68', 'Direct1D', 'link-68');">Direct1D</a></tt><tt class="py-op">(</tt><tt class="py-name">f</tt><tt class="py-op">,</tt> <tt class="py-number">3.21345</tt><tt class="py-op">,</tt> <tt class="py-name">emax</tt><tt class="py-op">=</tt><tt class="py-number">1e-12</tt><tt class="py-op">)</tt> </tt>
<a name="L559"></a><tt class="py-lineno">559</tt>  <tt class="py-line">    <tt class="py-keyword">print</tt> <tt id="link-69" class="py-name"><a title="peach.optm.linear" class="py-name" href="#" onclick="return doclink('link-69', 'linear', 'link-67');">linear</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L560"></a><tt class="py-lineno">560</tt>  <tt class="py-line">    <tt class="py-name">interp</tt> <tt class="py-op">=</tt> <tt id="link-70" class="py-name" targets="Class peach.optm.linear.Interpolation=peach.optm.linear.Interpolation-class.html"><a title="peach.optm.linear.Interpolation" class="py-name" href="#" onclick="return doclink('link-70', 'Interpolation', 'link-70');">Interpolation</a></tt><tt class="py-op">(</tt><tt class="py-name">f</tt><tt class="py-op">,</tt> <tt class="py-op">(</tt><tt class="py-number">0.</tt><tt class="py-op">,</tt> <tt class="py-number">0.75</tt><tt class="py-op">,</tt> <tt class="py-number">1.5</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">emax</tt><tt class="py-op">=</tt><tt class="py-number">1e-12</tt><tt class="py-op">)</tt> </tt>
<a name="L561"></a><tt class="py-lineno">561</tt>  <tt class="py-line">    <tt class="py-keyword">print</tt> <tt class="py-name">interp</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L562"></a><tt class="py-lineno">562</tt>  <tt class="py-line">    <tt class="py-name">golden</tt> <tt class="py-op">=</tt> <tt id="link-71" class="py-name" targets="Class peach.optm.linear.GoldenRule=peach.optm.linear.GoldenRule-class.html"><a title="peach.optm.linear.GoldenRule" class="py-name" href="#" onclick="return doclink('link-71', 'GoldenRule', 'link-71');">GoldenRule</a></tt><tt class="py-op">(</tt><tt class="py-name">f</tt><tt class="py-op">,</tt> <tt class="py-op">(</tt><tt class="py-number">0.75</tt><tt class="py-op">,</tt> <tt class="py-number">1.4</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">emax</tt><tt class="py-op">=</tt><tt class="py-number">1e-12</tt><tt class="py-op">)</tt> </tt>
<a name="L563"></a><tt class="py-lineno">563</tt>  <tt class="py-line">    <tt class="py-keyword">print</tt> <tt class="py-name">golden</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L564"></a><tt class="py-lineno">564</tt>  <tt class="py-line">    <tt class="py-name">fibo</tt> <tt class="py-op">=</tt> <tt id="link-72" class="py-name" targets="Class peach.optm.linear.Fibonacci=peach.optm.linear.Fibonacci-class.html"><a title="peach.optm.linear.Fibonacci" class="py-name" href="#" onclick="return doclink('link-72', 'Fibonacci', 'link-72');">Fibonacci</a></tt><tt class="py-op">(</tt><tt class="py-name">f</tt><tt class="py-op">,</tt> <tt class="py-op">(</tt><tt class="py-number">0.75</tt><tt class="py-op">,</tt> <tt class="py-number">1.4</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">emax</tt><tt class="py-op">=</tt><tt class="py-number">1e-12</tt><tt class="py-op">)</tt> </tt>
<a name="L565"></a><tt class="py-lineno">565</tt>  <tt class="py-line">    <tt class="py-keyword">print</tt> <tt class="py-name">fibo</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L566"></a><tt class="py-lineno">566</tt>  <tt class="py-line"> </tt><script type="text/javascript">
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